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The presence of sea ice leads in the sea ice cover represents a key feature in polar regions by controlling the heat exchange between the relatively warm ocean and cold atmosphere due to increased fluxes of turbulent sensible and latent heat. Sea ice leads contribute to the sea ice production and are sources for the formation of dense water which affects the ocean circulation. Atmospheric and ocean models strongly rely on observational data to describe the respective state of the sea ice since numerical models are not able to produce sea ice leads explicitly. For the Arctic, some lead datasets are available, but for the Antarctic, no such data yet exist. Our study presents a new algorithm with which leads are automatically identified in satellite thermal infrared images. A variety of lead metrics is used to distinguish between true leads and detection artefacts with the use of fuzzy logic. We evaluate the outputs and provide pixel-wise uncertainties. Our data yield daily sea ice lead maps at a resolution of 1 km2 for the winter months November– April 2002/03–2018/19 (Arctic) and April–September 2003–2019 (Antarctic), respectively. The long-term average of the lead frequency distributions show distinct features related to bathymetric structures in both hemispheres.
Ability self-concept (SC) and self-efficacy (SE) are central competence-related self-perceptions that affect students’ success in educational settings. Both constructs show conceptual differences but their empirical differentiation in higher education has not been sufficiently demonstrated. In the present study, we investigated the empirical differentiation of SC and SE in higher education with N = 1,243 German psychology students (81% female; age M = 23.62 years), taking into account central methodological requirements that, in part, have been neglected in prior studies. SC and SE were assessed at the same level of specificity, only cognitive SC items were used, and multiple academic domains were considered. We modeled the structure of SC and SE taking into account a multidimensional and/or hierarchical structure and investigated the empirical differentiation of both constructs on different levels of generality (i.e., domain-specific and domain-general). Results supported the empirical differentiation of SC and SE with medium-sized positive latent correlations (range r = .57 - .68) between SC and SE on different levels of generality. The knowledge about the internal structure of students’ SC and SE and the differentiation of both constructs can help us to develop construct-specific and domain-specific intervention strategies. Future empirical comparisons of the predictive power of SC and SE can provide further evidence that both represent empirical different constructs.
Although gravitropism forces trees to grow vertically, stems have shown to prefer specific orientations. Apart from wind deforming the tree shape, lateral light can result in prevailing inclination directions. In recent years a species dependent interaction between gravitropism and phototropism, resulting in trunks leaning down-slope, has been confirmed, but a terrestrial investigation of such factors is limited to small scale surveys. ALS offers the opportunity to investigate trees remotely. This study shall clarify whether ALS detected tree trunks can be used to identify prevailing trunk inclinations. In particular, the effect of topography, wind, soil properties and scan direction are investigated empirically using linear regression models. 299.000 significantly inclined stems were investigated. Species-specific prevailing trunk orientations could be observed. About 58% of the inclination and 19% of the orientation could be explained by the linear models, while the tree species, tree height, aspect and slope could be identified as significant factors. The models indicate that deciduous trees tend to lean down-slope, while conifers tend to lean leeward. This study has shown that ALS is suitable to investigate the trunk orientation on larger scales. It provides empirical evidence for the effect of phototropism and wind on the trunk orientation.
This study investigated correlative, factorial, and structural relationships between scores for ability emotional intelligence in the workplace (measured with the Geneva Emotional Competence Test), as well as fluid and crystallized abilities (measured with the Intelligence Structure Battery), carried out by a 188-participant student sample. Confirming existing research, recognition, understanding, and management of emotions were related primarily to crystallized ability tests measuring general knowledge, verbal fluency, and knowledge of word meaning. Meanwhile, emotion regulation was the least correlated with any other cognitive or emotional ability. In line with research on the trainability of emotional intelligence, these results may support the notion that emotional abilities are subject to acquired knowledge, where situational (i.e., workplace-specific) emotional intelligence may depend on accumulating relevant experiences.
The parameterization of the boundary layer is a challenge for regional climate models of the Arctic. In particular, the stable boundary layer (SBL) over Greenland, being the main driver for substantial katabatic winds over the slopes, is simulated differently by different regional climate models or using different parameterizations of the same model. However, verification data sets with high-resolution profiles of the katabatic wind are rare. In the present paper, detailed aircraft measurements of profiles in the katabatic wind and automatic weather station data during the experiment KABEG (Katabatic wind and boundary-layer front experiment around Greenland) in April and May 1997 are used for the verification of the regional climate model COSMO-CLM (CCLM) nested in ERA-Interim reanalyses. CCLM is used in a forecast mode for the whole Arctic with 15 km resolution and is run in the standard configuration of SBL parameterization and with modified SBL parameterization. In the modified version, turbulent kinetic energy (TKE) production and the transfer coefficients for turbulent fluxes in the SBL are reduced, leading to higher stability of the SBL. This leads to a more realistic representation of the daily temperature cycle and of the SBL structure in terms of temperature and wind profiles for the lowest 200 m.
B/ordering the Anthropocene: Inter- and Transdisciplinary Perspectives on Nature-Culture Relations
(2020)
In and with this thematic issue we would like to invite you to engage in productive boundary work and to critically examine the relationship between nature and culture in the Anthropocene. A few years ago, the term Anthropocene was proposed by Paul Crutzen as a term for the current geological epoch, in which humankind (the ‘anthropos’) is seen as the central driving force for global changes in ecological systems. This epoch is characterized by the blurring of boundaries between society and nature, science and politics, as well as by the increased drawing of boundaries between social groups, lifestyles, and the Global North and Global South. With this issue, we would like to give an impetus to explore boundary phenomena in the relationship between nature and society, which up to now have not been the focus of Border Studies. The challenges and problems of the Anthropocene require cross-border thinking and research that stimulates a new reflexivity and commitment, to which the multidisciplinary field of Border Studies can contribute.
The object of the current Thematic Issue is not to focus on the individuals (the cross-border commuters) but on the organization of the cross-border labor markets. We move from a micro perspective to a macro perspective in order to underline the diversity of the cross-border labor markets (at the French borders, for example) and shed light on the many aspects that impact cross-border supply or demand. Trying to understand the whole system that goes beyond the cross-border flows, the question we address in this thematic issue is about the organization of the labor markets: is the system organized in a cross-border way? Or do the borders still prevent a genuinely integrated cross-border labor market?
Estimation and therefore prediction -- both in traditional statistics and machine learning -- encounters often problems when done on survey data, i.e. on data gathered from a random subset of a finite population. Additional to the stochastic generation of the data in the finite population (based on a superpopulation model), the subsetting represents a second randomization process, and adds further noise to the estimation. The character and impact of the additional noise on the estimation procedure depends on the specific probability law for subsetting, i.e. the survey design. Especially when the design is complex or the population data is not generated by a Gaussian distribution, established methods must be re-thought. Both phenomena can be found in business surveys, and their combined occurrence poses challenges to the estimation.
This work introduces selected topics linked to relevant use cases of business surveys and discusses the role of survey design therein: First, consider micro-econometrics using business surveys. Regression analysis under the peculiarities of non-normal data and complex survey design is discussed. The focus lies on mixed models, which are able to capture unobserved heterogeneity e.g. between economic sectors, when the dependent variable is not conditionally normally distributed. An algorithm for survey-weighted model estimation in this setting is provided and applied to business data.
Second, in official statistics, the classical sampling randomization and estimators for finite population totals are relevant. The variance estimation of estimators for (finite) population totals plays a major role in this framework in order to decide on the reliability of survey data. When the survey design is complex, and the number of variables is large for which an estimated total is required, generalized variance functions are popular for variance estimation. They allow to circumvent cumbersome theoretical design-based variance formulae or computer-intensive resampling. A synthesis of the superpopulation-based motivation and the survey framework is elaborated. To the author's knowledge, such a synthesis is studied for the first time both theoretically and empirically.
Third, the self-organizing map -- an unsupervised machine learning algorithm for data visualization, clustering and even probability estimation -- is introduced. A link to Markov random fields is outlined, which to the author's knowledge has not yet been established, and a density estimator is derived. The latter is evaluated in terms of a Monte-Carlo simulation and then applied to real world business data.
Designing a Randomized Trial with an Age Simulation Suit—Representing People with Health Impairments
(2020)
Due to demographic change, there is an increasing demand for professional care services, whereby this demand cannot be met by available caregivers. To enable adequate care by relieving informal and formal care, the independence of people with chronic diseases has to be preserved for as long as possible. Assistance approaches can be used that support promoting physical activity, which is a main predictor of independence. One challenge is to design and test such approaches without affecting the people in focus. In this paper, we propose a design for a randomized trial to enable the use of an age simulation suit to generate reference data of people with health impairments with young and healthy participants. Therefore, we focus on situations of increased physical activity.
Retirement, fertility and sexuality are three key life stage events that are embedded in the framework of population economics in this dissertation. Each topic implies economic relevance. As retirement entry shifts labour supply of experienced workers to zero, this issue is particularly relevant for employers, retirees themselves as well as policymakers who are in charge of the design of the pension system. Giving birth has comprehensive economic relevance for women. Parental leave and subsequent part-time work lead to a direct loss of income. Lower levels of employment, work experience, training and career opportunities result in indirect income losses. Sexuality has decisive influence on the quality of partnerships, subjective well-being and happiness. Well-being and happiness, in turn, are significant key determinants not only in private life but also in the work domain, for example in the area of job performance. Furthermore, partnership quality determines the duration of a partnership. And in general, partnerships enable the pooling of (financial) resources - compared to being single. The contribution of this dissertation emerges from the integration of social and psychological concepts into economic analysis as well as the application of economic theory in non-standard economic research topics. The results of the three chapters show that the multidisciplinary approach yields better prediction of human behaviour than the single disciplines on their own. The results in the first chapter show that both interpersonal conflict with superiors and the individual’s health status play a significant role in retirement decisions. The chapter further contributes to existing literature by showing the moderating role of health within the retirement decision-making: On the one hand, all employees are more likely to retire when they are having conflicts with their superior. On the other hand, among healthy employees, the same conflict raises retirement intentions even more. That means good health is a necessary, but not a sufficient condition for continued working. It may be that conflicts with superiors raise retirement intentions more if the worker is healthy. The key findings of the second chapter reveal significant influence of religion on contraceptive and fertility-related decisions. A large part of research on religion and fertility is originated in evidence from the US. This chapter contrasts evidence from Germany. Additionally, the chapter contributes by integrating miscarriages and abortions, rather than limiting the analysis to births and it gains from rich prospective data on fertility biography of women. The third chapter provides theoretical insights on how to incorporate psychological variables into an economic framework which aims to analyse sexual well-being. According to this theory, personality may play a dual role by shaping a person’s preferences for sex as well as the person’s behaviour in a sexual relationship. Results of econometric analysis reveal detrimental effects of neuroticism on sexual well-being while conscientiousness seems to create a win-win situation for a couple. Extraversions and Openness have ambiguous effects on romantic relationships by enhancing sexual well-being on the one hand but raising commitment problems on the other. Agreeable persons seem to gain sexual satisfaction even if they perform worse in sexual communication.
A lack of ability to inhibit prepotent responses, or more generally a lack of impulse control, is associated with several disorders such as attention-deficit/hyperactivity disorder and schizophrenia as well as general damage to the prefrontal cortex. A stop-signal task (SST) is a reliable and established measure of response inhibition. However, using the SST as an objective assessment in diagnostic or research-focused settings places significant stress on participants as the task itself requires concentration and cognitive effort and is not particularly engaging. This can lead to decreased motivation to follow task instructions and poor data quality, which can affect assessment efficacy and might increase drop-out rates. Gamification—the application of game-based elements in nongame settings—has shown to improve engaged attention to a cognitive task, thus increasing participant motivation and data quality.
Imagery-based techniques have received increasing interest in psychotherapy research. Whereas their effectiveness has been shown for various psychological disorders, their underlying mechanisms remain unclear. Current research predominantly investigates intrapersonal processes, while interpersonal processes have received no attention to date. The aim of the current dissertation was to fill this lacuna. The three interrelated studies comprising this dissertation were the first to examine the effectiveness of imagery-based techniques in the treatment of test anxiety, relate physiological arousal to emotional processing, and investigate the association between physiological synchrony and multiple process measures.
Study I investigated the feasibility of a newly developed protocol, which integrates imagery-based and cognitive-behavioral components, to treat test anxiety in a sample of 31 students. The results indicated the protocol as acceptable, feasible, and effective in the treatment of test anxiety. Additionally, the imagery-based component was positively associated with therapeutic bond, session evaluation, and emotional experience.
Study II shifted the focus from the effectiveness of imagery-based techniques to client-therapist physiological synchrony as a putative mechanism of change in the same sample. The results suggested that physiological synchrony was greater than chance during both imagery-based and cognitive-behavioral components. Variability of physiological synchrony on the session-level during the imagery-based components and variability on both levels (session and dyad) during the cognitive-behavioral components were demonstrated. Furthermore, physiological synchrony of the imagery-based segments was positively assocatied with therapeutic bond. No association was found for the cognitive-behavioral components.
Study III examined both intrapersonal (i.e., clients’ electrodermal activity) and interpersonal (i.e., client-therapist electrodermal activity synchrony) processes and their associations with emotional processing in a sample of 49 client-therapist-dyads. The results suggested that higher client physiological arousal and a moderate level of physiological synchrony were associated with deeper emotional processing.
Taken together, the results highlight the effectiveness of imagery-based techniques in the treatment of test anxiety. Furthermore, the results of Studies II and III support the idea of physiological synchrony as a mechanism of change in imagery with and without rescripting. The current dissertation takes an important step towards optimizing process research within psychotherapy and contributes to a better understanding of the potency and mechanisms of change of imagery-based techniques. We hope that these studies’ implications will support everyday clinical practice.
Primary focal hyperhidrosis (PFH, OMIM %144110) is a genetically influenced condition characterised by excessive sweating. Prevalence varies between 1.0–6.1% in the general population, dependent on ethnicity. The aetiology of PFH remains unclear but an autosomal dominant mode of inheritance, incomplete penetrance and variable phenotypes have been reported. In our study, nine pedigrees (50 affected, 53 non-affected individuals) were included. Clinical characterisation was performed at the German Hyperhidrosis Centre, Munich, by using physiological and psychological questionnaires. Genome-wide parametric linkage analysis with GeneHunter was performed based on the Illumina genome-wide SNP arrays. Haplotypes were constructed using easyLINKAGE and visualised via HaploPainter. Whole-exome sequencing (WES) with 100x coverage in 31 selected members (24 affected, 7 non-affected) from our pedigrees was achieved by next generation sequencing. We identified four genome-wide significant loci, 1q41-1q42.3, 2p14-2p13.3, 2q21.2-2q23.3 and 15q26.3-15q26.3 for PFH. Three pedigrees map to a shared locus at 2q21.2-2q23.3, with a genome-wide significant LOD score of 3.45. The chromosomal region identified here overlaps with a locus at chromosome 2q22.1-2q31.1 reported previously. Three families support 1q41-1q42.3 (LOD = 3.69), two families share a region identical by descent at 2p14-2p13.3 (LOD = 3.15) and another two families at 15q26.3 (LOD = 3.01). Thus, our results point to considerable genetic heterogeneity. WES did not reveal any causative variants, suggesting that variants or mutations located outside the coding regions might be involved in the molecular pathogenesis of PFH. We suggest a strategy based on whole-genome or targeted next generation sequencing to identify causative genes or variants for PFH.
The dissertation includes three published articles on which the development of a theoretical model of motivational and self-regulatory determinants of the intention to comprehensively search for health information is based. The first article focuses on building a solid theoretical foundation as to the nature of a comprehensive search for health information and enabling its integration into a broader conceptual framework. Based on subjective source perceptions, a taxonomy of health information sources was developed. The aim of this taxonomy was to identify most fundamental source characteristics to provide a point of reference when it comes to relating to the target objects of a comprehensive search. Three basic source characteristics were identified: expertise, interaction and accessibility. The second article reports on the development and evaluation of an instrument measuring the goals individuals have when seeking health information: the ‘Goals Associated with Health Information Seeking’ (GAINS) questionnaire. Two goal categories (coping focus and regulatory focus) were theoretically derived, based on which four goals (understanding, action planning, hope and reassurance) were classified. The final version of the questionnaire comprised four scales representing the goals, with four items per scale (sixteen items in total). The psychometric properties of the GAINS were analyzed in three independent samples, and the questionnaire was found to be reliable and sufficiently valid as well as suitable for a patient sample. It was concluded that the GAINS makes it possible to evaluate goals of health information seeking (HIS) which are likely to inform the intention building on how to organize the search for health information. The third article describes the final development and a first empirical evaluation of a model of motivational and self-regulatory determinants of an intentionally comprehensive search for health information. Based on the insights and implications of the previous two articles and an additional rigorous theoretical investigation, the model included approach and avoidance motivation, emotion regulation, HIS self-efficacy, problem and emotion focused coping goals and the intention to seek comprehensively (as outcome variable). The model was analyzed via structural equation modeling in a sample of university students. Model fit was good and hypotheses with regard to specific direct and indirect effects were confirmed. Last, the findings of all three articles are synthesized, the final model is presented and discussed with regard to its strengths and weaknesses, and implications for further research are determined.
Up-to-date information about the type and spatial distribution of forests is an essential element in both sustainable forest management and environmental monitoring and modelling. The OpenStreetMap (OSM) database contains vast amounts of spatial information on natural features, including forests (landuse=forest). The OSM data model includes describing tags for its contents, i.e., leaf type for forest areas (i.e., leaf_type=broadleaved). Although the leaf type tag is common, the vast majority of forest areas are tagged with the leaf type mixed, amounting to a total area of 87% of landuse=forests from the OSM database. These areas comprise an important information source to derive and update forest type maps. In order to leverage this information content, a methodology for stratification of leaf types inside these areas has been developed using image segmentation on aerial imagery and subsequent classification of leaf types. The presented methodology achieves an overall classification accuracy of 85% for the leaf types needleleaved and broadleaved in the selected forest areas. The resulting stratification demonstrates that through approaches, such as that presented, the derivation of forest type maps from OSM would be feasible with an extended and improved methodology. It also suggests an improved methodology might be able to provide updates of leaf type to the OSM database with contributor participation.
Many NP-hard optimization problems that originate from classical graph theory, such as the maximum stable set problem and the maximum clique problem, have been extensively studied over the past decades and involve the choice of a subset of edges or vertices. There usually exist combinatorial methods that can be applied to solve them directly in the graph.
The most simple method is to enumerate feasible solutions and select the best. It is not surprising that this method is very slow oftentimes, so the task is to cleverly discard fruitless search space during the search. An alternative method to solve graph problems is to formulate integer linear programs, such that their solution yields an optimal solution to the original optimization problem in the graph. In order to solve integer linear programs, one can start with relaxing the integer constraints and then try to find inequalities for cutting off fractional extreme points. In the best case, it would be possible to describe the convex hull of the feasible region of the integer linear program with a set of inequalities. In general, giving a complete description of this convex hull is out of reach, even if it has a polynomial number of facets. Thus, one tries to strengthen the (weak) relaxation of the integer linear program best possible via strong inequalities that are valid for the convex hull of feasible integer points.
Many classes of valid inequalities are of exponential size. For instance, a graph can have exponentially many odd cycles in general and therefore the number of odd cycle inequalities for the maximum stable set problem is exponential. It is sometimes possible to check in polynomial time if some given point violates any of the exponentially many inequalities. This is indeed the case for the odd cycle inequalities for the maximum stable set problem. If a polynomial time separation algorithm is known, there exists a formulation of polynomial size that contains a given point if and only if it does not violate one of the (potentially exponentially many) inequalities. This thesis can be divided into two parts. The first part is the main part and it contains various new results. We present new extended formulations for several optimization problems, i.e. the maximum stable set problem, the nonconvex quadratic program with box
constraints and the p-median problem. In the second part we modify a very fast algorithm for finding a maximum clique in very large sparse graphs. We suggest and compare three alternative versions of this algorithm to the original version and compare their strengths and weaknesses.
This work studies typical mathematical challenges occurring in the modeling and simulation of manufacturing processes of paper or industrial textiles. In particular, we consider three topics: approximate models for the motion of small inertial particles in an incompressible Newtonian fluid, effective macroscopic approximations for a dilute particle suspension contained in a bounded domain accounting for a non-uniform particle distribution and particle inertia, and possibilities for a reduction of computational cost in the simulations of slender elastic fibers moving in a turbulent fluid flow.
We consider the full particle-fluid interface problem given in terms of the Navier-Stokes equations coupled to momentum equations of a small rigid body. By choosing an appropriate asymptotic scaling for the particle-fluid density ratio and using an asymptotic expansion for the solution components, we derive approximations of the original interface problem. The approximate systems differ according to the chosen scaling of the density ratio in their physical behavior allowing the characterization of different inertial regimes.
We extend the asymptotic approach to the case of many particles suspended in a Newtonian fluid. Under specific assumptions for the combination of particle size and particle number, we derive asymptotic approximations of this system. The approximate systems describe the particle motion which allows to use a mean field approach in order to formulate the continuity equation for the particle probability density function. The coupling of the latter with the approximation for the fluid momentum equation then reveals a macroscopic suspension description which accounts for non-uniform particle distributions in space and for small particle inertia.
A slender fiber in a turbulent air flow can be modeled as a stochastic inextensible one-dimensionally parametrized Kirchhoff beam, i.e., by a stochastic partial differential algebraic equation. Its simulations involve the solution of large non-linear systems of equations by Newton's method. In order to decrease the computational time, we explore different methods for the estimation of the solution. Additionally, we apply smoothing techniques to the Wiener Process in order to regularize the stochastic force driving the fiber, exploring their respective impact on the solution and performance. We also explore the applicability of the Wiener chaos expansion as a solution technique for the simulation of the fiber dynamics.
In this thesis we study structure-preserving model reduction methods for the efficient and reliable approximation of dynamical systems. A major focus is the approximation of a nonlinear flow problem on networks, which can, e.g., be used to describe gas network systems. Our proposed approximation framework guarantees so-called port-Hamiltonian structure and is general enough to be realizable by projection-based model order reduction combined with complexity reduction. We divide the discussion of the flow problem into two parts, one concerned with the linear damped wave equation and the other one with the general nonlinear flow problem on networks.
The study around the linear damped wave equation relies on a Galerkin framework, which allows for convenient network generalizations. Notable contributions of this part are the profound analysis of the algebraic setting after space-discretization in relation to the infinite dimensional setting and its implications for model reduction. In particular, this includes the discussion of differential-algebraic structures associated to the network-character of our problem and the derivation of compatibility conditions related to fundamental physical properties. Amongst the different model reduction techniques, we consider the moment matching method to be a particularly well-suited choice in our framework.
The Galerkin framework is then appropriately extended to our general nonlinear flow problem. Crucial supplementary concepts are required for the analysis, such as the partial Legendre transform and a more careful discussion of the underlying energy-based modeling. The preservation of the port-Hamiltonian structure after the model-order- and complexity-reduction-step represents a major focus of this work. Similar as in the analysis of the model order reduction, compatibility conditions play a crucial role in the analysis of our complexity reduction, which relies on a quadrature-type ansatz. Furthermore, energy-stable time-discretization schemes are derived for our port-Hamiltonian approximations, as structure-preserving methods from literature are not applicable due to our rather unconventional parametrization of the solution.
Apart from the port-Hamiltonian approximation of the flow problem, another topic of this thesis is the derivation of a new extension of moment matching methods from linear systems to quadratic-bilinear systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate frequency representations tailored towards user-defined families of inputs. Then moment matching corresponds to a one-dimensional interpolation problem rather than to a multi-dimensional interpolation as for the multivariate approaches, i.e., it involves fewer interpolation frequencies to be chosen. The notion of signal-generator-driven systems, variational expansions of the resulting autonomous systems as well as the derivation of convenient tensor-structured approximation conditions are the main ingredients of this part. Notably, our approach allows for the incorporation of general input relations in the state equations, not only affine-linear ones as in existing system-theoretic methods.
Traditionell werden Zufallsstichprobenerhebungen so geplant, dass nationale Statistiken zuverlässig mit einer adäquaten Präzision geschätzt werden können. Hierbei kommen vorrangig designbasierte, Modell-unterstützte (engl. model assisted) Schätzmethoden zur Anwendung, die überwiegend auf asymptotischen Eigenschaften beruhen. Für kleinere Stichprobenumfänge, wie man sie für Small Areas (Domains bzw. Subpopulationen) antrifft, eignen sich diese Schätzmethoden eher nicht, weswegen für diese Anwendung spezielle modellbasierte Small Area-Schätzverfahren entwickelt wurden. Letztere können zwar Verzerrungen aufweisen, besitzen jedoch häufig einen kleineren mittleren quadratischen Fehler der Schätzung als dies für designbasierte Schätzer der Fall ist. Den Modell-unterstützten und modellbasierten Methoden ist gemeinsam, dass sie auf statistischen Modellen beruhen; allerdings in unterschiedlichem Ausmass. Modell-unterstützte Verfahren sind in der Regel so konstruiert, dass der Beitrag des Modells bei sehr grossen Stichprobenumfängen gering ist (bei einer Grenzwertbetrachtung sogar wegfällt). Bei modellbasierten Methoden nimmt das Modell immer eine tragende Rolle ein, unabhängig vom Stichprobenumfang. Diese Überlegungen veranschaulichen, dass das unterstellte Modell, präziser formuliert, die Güte der Modellierung für die Qualität der Small Area-Statistik von massgeblicher Bedeutung ist. Wenn es nicht gelingt, die empirischen Daten durch ein passendes Modell zu beschreiben und mit den entsprechenden Methoden zu schätzen, dann können massive Verzerrungen und / oder ineffiziente Schätzungen resultieren.
Die vorliegende Arbeit beschäftigt sich mit der zentralen Frage der Robustheit von Small Area-Schätzverfahren. Als robust werden statistische Methoden dann bezeichnet, wenn sie eine beschränkte Einflussfunktion und einen möglichst hohen Bruchpunkt haben. Vereinfacht gesprochen zeichnen sich robuste Verfahren dadurch aus, dass sie nur unwesentlich durch Ausreisser und andere Anomalien in den Daten beeinflusst werden. Die Untersuchung zur Robustheit konzentriert sich auf die folgenden Modelle bzw. Schätzmethoden:
i) modellbasierte Schätzer für das Fay-Herriot-Modell (Fay und Herrot, 1979, J. Amer. Statist. Assoc.) und das elementare Unit-Level-Modell (vgl. Battese et al., 1988, J. Amer. Statist. Assoc.).
ii) direkte, Modell-unterstützte Schätzer unter der Annahme eines linearen Regressionsmodells.
Das Unit-Level-Modell zur Mittelwertschätzung beruht auf einem linearen gemischten Gauss'schen Modell (engl. mixed linear model, MLM) mit blockdiagonaler Kovarianzmatrix. Im Gegensatz zu bspw. einem multiplen linearen Regressionsmodell, besitzen MLM-Modelle keine nennenswerten Invarianzeigenschaften, so dass eine Kontamination der abhängigen Variablen unvermeidbar zu verzerrten Parameterschätzungen führt. Für die Maximum-Likelihood-Methode kann die resultierende Verzerrung nahezu beliebig groß werden. Aus diesem Grund haben Richardson und Welsh (1995, Biometrics) die robusten Schätzmethoden RML 1 und RML 2 entwickelt, die bei kontaminierten Daten nur eine geringe Verzerrung aufweisen und wesentlich effizienter sind als die Maximum-Likelihood-Methode. Eine Abwandlung von Methode RML 2 wurde Sinha und Rao (2009, Canad. J. Statist.) für die robuste Schätzung von Unit-Level-Modellen vorgeschlagen. Allerdings erweisen sich die gebräuchlichen numerischen Verfahren zur Berechnung der RML-2-Methode (dies gilt auch für den Vorschlag von Sinha und Rao) als notorisch unzuverlässig. In dieser Arbeit werden zuerst die Konvergenzprobleme der bestehenden Verfahren erörtert und anschließend ein numerisches Verfahren vorgeschlagen, das sich durch wesentlich bessere numerische Eigenschaften auszeichnet. Schließlich wird das vorgeschlagene Schätzverfahren im Rahmen einer Simulationsstudie untersucht und anhand eines empirischen Beispiels zur Schätzung von oberirdischer Biomasse in norwegischen Kommunen illustriert.
Das Modell von Fay-Herriot kann als Spezialfall eines MLM mit blockdiagonaler Kovarianzmatrix aufgefasst werden, obwohl die Varianzen des Zufallseffekts für die Small Areas nicht geschätzt werden müssen, sondern als bereits bekannte Größen betrachtet werden. Diese Eigenschaft kann man sich nun zunutze machen, um die von Sinha und Rao (2009) vorgeschlagene Robustifizierung des Unit-Level-Modells direkt auf das Fay-Herriot Model zu übertragen. In der vorliegenden Arbeit wird jedoch ein alternativer Vorschlag erarbeitet, der von der folgenden Beobachtung ausgeht: Fay und Herriot (1979) haben ihr Modell als Verallgemeinerung des James-Stein-Schätzers motiviert, wobei sie sich einen empirischen Bayes-Ansatz zunutze machen. Wir greifen diese Motivation des Problems auf und formulieren ein analoges robustes Bayes'sches Verfahren. Wählt man nun in der robusten Bayes'schen Problemformulierung die ungünstigste Verteilung (engl. least favorable distribution) von Huber (1964, Ann. Math. Statist.) als A-priori-Verteilung für die Lokationswerte der Small Areas, dann resultiert als Bayes-Schätzer [=Schätzer mit dem kleinsten Bayes-Risk] die Limited-Translation-Rule (LTR) von Efron und Morris (1971, J. Amer. Statist. Assoc.). Im Kontext der frequentistischen Statistik kann die Limited-Translation-Rule nicht verwendet werden, weil sie (als Bayes-Schätzer) auf unbekannten Parametern beruht. Die unbekannten Parameter können jedoch nach dem empirischen Bayes-Ansatz an der Randverteilung der abhängigen Variablen geschätzt werden. Hierbei gilt es zu beachten (und dies wurde in der Literatur vernachlässigt), dass die Randverteilung unter der ungünstigsten A-priori-Verteilung nicht einer Normalverteilung entspricht, sondern durch die ungünstigste Verteilung nach Huber (1964) beschrieben wird. Es ist nun nicht weiter erstaunlich, dass es sich bei den Maximum-Likelihood-Schätzern von Regressionskoeffizienten und Modellvarianz unter der Randverteilung um M-Schätzer mit der Huber'schen psi-Funktion handelt.
Unsere theoriegeleitete Herleitung von robusten Schätzern zum Fay-Herriot-Modell zeigt auf, dass bei kontaminierten Daten die geschätzte LTR (mit Parameterschätzungen nach der M-Schätzmethodik) optimal ist und, dass die LTR ein integraler Bestandteil der Schätzmethodik ist (und nicht als ``Zusatz'' o.Ä. zu betrachten ist, wie dies andernorts getan wird). Die vorgeschlagenen M-Schätzer sind robust bei Vorliegen von atypischen Small Areas (Ausreissern), wie dies auch die Simulations- und Fallstudien zeigen. Um auch Robustheit bei Vorkommen von einflussreichen Beobachtungen in den unabhängigen Variablen zu erzielen, wurden verallgemeinerte M-Schätzer (engl. generalized M-estimator) für das Fay-Herriot-Modell entwickelt.
Currently, new business models created in the sharing economy differ considerably and they differ in the formation of trust as well. If and how trust can be created is shown by a comparison of two examples which diverge in their founding philosophy. The chosen example of community-based economy, Community Supported Agriculture (CSA), no longer trusts the capitalist system and therefore distances itself and creates its own environment including a new business model. It is implemented within rather small groups where trust is created by personal relations and face-to-face communication. On the contrary, the example of a platform economy, the accommodation-provider company Airbnb, shows trust in the system and pushes technological innovations through the use of platform applications. It promotes trust and confidence in the progress of technology. For the conceptual analysis, the distinction between personal trust and system trust defined by Niklas Luhmann is adopted. The analysis describes two different modes of trust formation and how they push distrust or improve trust. Grounded on these analyses, assumptions on the process of trust formation within varying models of the sharing economy are formulated as well as a hypothesis about possible developments is introduced for further research.