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Official business surveys form the basis for national and regional business statistics and are thus of great importance for analysing the state and performance of the economy. However, both the heterogeneity of business data and their high dynamics pose a particular challenge to the feasibility of sampling and the quality of the resulting estimates. A widely used sampling frame for creating the design of an official business survey is an extract from an official business register. However, if this frame does not accurately represent the target population, frame errors arise. Amplified by the heterogeneity and dynamics of business populations, these errors can significantly affect the estimation quality and lead to inefficiencies and biases. This dissertation therefore deals with design-based methods for optimising business surveys with respect to different types of frame errors.
First, methods for adjusting the sampling design of business surveys are addressed. These approaches integrate auxiliary information about the expected structures of frame errors into the sampling design. The aim is to increase the number of sampled businesses that are subject to frame errors. The element-specific frame error probability is estimated based on auxiliary information about frame errors observed in previous samples. The approaches discussed consider different types of frame errors and can be incorporated into predefined designs with fixed strata.
As the second main pillar of this work, methods for adjusting weights to correct for frame errors during estimation are developed and investigated. As a result of frame errors, the assumptions under which the original design weights were determined based on the sampling design no longer hold. The developed methods correct the design weights taking into account the errors identified for sampled elements. Case-number-based reweighting approaches, on the one hand, attempt to reconstruct the unknown size of the individual strata in the target population. In the context of weight smoothing methods, on the other hand, design weights are modelled and smoothed as a function of target or auxiliary variables. This serves to avoid inefficiencies in the estimation due to highly scattering weights or weak correlations between weights and target variables. In addition, possibilities of correcting frame errors by calibration weighting are elaborated. Especially when the sampling frame shows over- and/or undercoverage, the inclusion of external auxiliary information can provide a significant improvement of the estimation quality. For those methods whose quality cannot be measured using standard procedures, a procedure for estimating the variance based on a rescaling bootstrap is proposed. This enables an assessment of the estimation quality when using the methods in practice.
In the context of two extensive simulation studies, the methods presented in this dissertation are evaluated and compared with each other. First, in the environment of an experimental simulation, it is assessed which approaches are particularly suitable with regard to different data situations. In a second simulation study, which is based on the structural survey in the services sector, the applicability of the methods in practice is evaluated under realistic conditions.
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.
This dissertation investigates corporate acquisition decisions that represent important corporate development activities for family and non-family firms. The main research objective of this dissertation is to generate insights into the subjective decision-making behavior of corporate decision-makers from family and non-family firms and their weighting of M&A decision-criteria during the early pre-acquisition target screening and selection process. The main methodology chosen for the investigation of M&A decision-making preferences and the weighting of M&A decision criteria is a choice-based conjoint analysis. The overall sample of this dissertation consists of 304 decision-makers from 264 private and public family and non-family firms from mainly Germany and the DACH-region. In the first empirical part of the dissertation, the relative importance of strategic, organizational and financial M&A decision-criteria for corporate acquirers in acquisition target screening is investigated. In addition, the author uses a cluster analysis to explore whether distinct decision-making patterns exist in acquisition target screening. In the second empirical part, the dissertation explores whether there are differences in investment preferences in acquisition target screening between family and non-family firms and within the group of family firms. With regards to the heterogeneity of family firms, the dissertation generated insights into how family-firm specific characteristics like family management, the generational stage of the firm and non-economic goals such as transgenerational control intention influences the weighting of different M&A decision criteria in acquisition target screening. The dissertation contributes to strategic management research, in specific to M&A literature, and to family business research. The results of this dissertation generate insights into the weighting of M&A decision-making criteria and facilitate a better understanding of corporate M&A decisions in family and non-family firms. The findings show that decision-making preferences (hence the weighting of M&A decision criteria) are influenced by characteristics of the individual decision-maker, the firm and the environment in which the firm operates.
In order to classify smooth foliated manifolds, which are smooth maifolds equipped with a smooth foliation, we introduce the de Rham cohomologies of smooth foliated manifolds. These cohomologies are build in a similar way as the de Rham cohomologies of smooth manifolds. We develop some tools to compute these cohomologies. For example we proof a Mayer Vietoris theorem for foliated de Rham cohomology and show that these cohomologys are invariant under integrable homotopy. A generalization of a known Künneth formula, which relates the cohomologies of a product foliation with its factors, is discussed. In particular, this envolves a splitting theory of sequences between Frechet spaces and a theory of projective spectrums. We also prove, that the foliated de Rham cohomology is isomorphic to the Cech-de Rham cohomology and the Cech cohomology of leafwise constant functions of an underlying so called good cover.
This work deals with the current support landscape for Social Entrepreneurship (SE) in the DACH region. It provides answers to the questions of which actors support SE, how and why they do so, and which social ventures are supported. In addition, there is a focus on the motives for supporting SE as well as the decision-making process while selecting social ventures. In both cases, it is examined whether certain characteristics of the decision-maker and the organization influence the weighting of motives and decision-making criteria. More precise, the gender of the decision-maker as well as the kind of support by the organization is analyzed. The concrete examples of foundations and venture philanthropy organizations (VPOs) will give a deeper look at the SE support motives and decision-making behavior. In a quantitative empirical data collection, by means of an online survey, decision-makers from SE supporting organizations in the DACH region were asked to participate in a conjoint experiment and to fill in a questionnaire. The results illustrate a positive development of the SE support landscape in the German-speaking area as well as the heterogeneity of the organizational types, the financial and non-financial support instruments and the supported social ventures. Regarding the motives for SE-support, a general endeavor to change and to create an impact has proven to be particularly important at the organizational and the individual level. At the individual level female and male decision-makers have subtle differences in their motives to promote SE. Robustness checks by analyzing certain subsamples provide information about that. Individuals from foundations and VPOs, on the other hand, hardly differ from each other, even though here individuals with a rather social background face individuals with a business background. At the organizational level crucial differences can be identified for the motives, depending on the nature of the organization's support, and again comparing foundations with VPOs. Especially for the motives 'financial interests', 'reputation' and 'employee development' there are big differences between the considered groups. Eventually, by means of cluster analysis and still with respect to the support motives, two types of decision-makers could be determined on both the individual and the organizational level.
In terms of the decision-making behavior, and the weighting of certain decision-making criteria respectively, it has emerged that it is worthwhile having a closer look: The 'importance of the social problem' and the 'authenticity of the start-up team' are consistently the two most important criteria when it comes to selecting social ventures for supporting them. However, comparing male and female decision-makers, foundations and VPOs, as well as the two groups of financially and non-financially supporting organizations, there are certain specifics which are highly relevant for SE practice. Here as well a cluster analysis uncovered patterns of criteria weighting by identifying three different types of decision-makers.
Surveys play a major role in studying social and behavioral phenomena that are difficult to
observe. Survey data provide insights into the determinants and consequences of human
behavior and social interactions. Many domains rely on high quality survey data for decision
making and policy implementation including politics, health, business, and the social
sciences. Given a certain research question in a specific context, finding the most appropriate
survey design to ensure data quality and keep fieldwork costs low at the same time is a
difficult task. The aim of examining survey research methodology is to provide the best
evidence to estimate the costs and errors of different survey design options. The goal of this
thesis is to support and optimize the accumulation and sustainable use of evidence in survey
methodology in four steps:
(1) Identifying the gaps in meta-analytic evidence in survey methodology by a systematic
review of the existing evidence along the dimensions of a central framework in the
field
(2) Filling in these gaps with two meta-analyses in the field of survey methodology, one
on response rates in psychological online surveys, the other on panel conditioning
effects for sensitive items
(3) Assessing the robustness and sufficiency of the results of the two meta-analyses
(4) Proposing a publication format for the accumulation and dissemination of metaanalytic
evidence
Many combinatorial optimization problems on finite graphs can be formulated as conic convex programs, e.g. the stable set problem, the maximum clique problem or the maximum cut problem. Especially NP-hard problems can be written as copositive programs. In this case the complexity is moved entirely into the copositivity constraint.
Copositive programming is a quite new topic in optimization. It deals with optimization over the so-called copositive cone, a superset of the positive semidefinite cone, where the quadratic form x^T Ax has to be nonnegative for only the nonnegative vectors x. Its dual cone is the cone of completely positive matrices, which includes all matrices that can be decomposed as a sum of nonnegative symmetric vector-vector-products.
The related optimization problems are linear programs with matrix variables and cone constraints.
However, some optimization problems can be formulated as combinatorial problems on infinite graphs. For example, the kissing number problem can be formulated as a stable set problem on a circle.
In this thesis we will discuss how the theory of copositive optimization can be lifted up to infinite dimension. For some special cases we will give applications in combinatorial optimization.
This dissertation deals with consistent estimates in household surveys. Household surveys are often drawn via cluster sampling, with households sampled at the first stage and persons selected at the second stage. The collected data provide information for estimation at both the person and the household level. However, consistent estimates are desirable in the sense that the estimated household-level totals should coincide with the estimated totals obtained at the person-level. Current practice in statistical offices is to use integrated weighting. In this approach consistent estimates are guaranteed by equal weights for all persons within a household and the household itself. However, due to the forced equality of weights, the individual patterns of persons are lost and the heterogeneity within households is not taken into account. In order to avoid the negative consequences of integrated weighting, we propose alternative weighting methods in the first part of this dissertation that ensure both consistent estimates and individual person weights within a household. The underlying idea is to limit the consistency conditions to variables that emerge in both the personal and household data sets. These common variables are included in the person- and household-level estimator as additional auxiliary variables. This achieves consistency more directly and only for the relevant variables, rather than indirectly by forcing equal weights on all persons within a household. Further decisive advantages of the proposed alternative weighting methods are that original individual rather than the constructed aggregated auxiliaries are utilized and that the variable selection process is more flexible because different auxiliary variables can be incorporated in the person-level estimator than in the household-level estimator.
In the second part of this dissertation, the variances of a person-level GREG estimator and an integrated estimator are compared in order to quantify the effects of the consistency requirements in the integrated weighting approach. One of the challenges is that the estimators to be compared are of different dimensions. The proposed solution is to decompose the variance of the integrated estimator into the variance of a reduced GREG estimator, whose underlying model is of the same dimensions as the person-level GREG estimator, and add a constructed term that captures the effects disregarded by the reduced model. Subsequently, further fields of application for the derived decomposition are proposed such as the variable selection process in the field of econometrics or survey statistics.
Differential equations yield solutions that necessarily contain a certain amount of regularity and are based on local interactions. There are various natural phenomena that are not well described by local models. An important class of models that describe long-range interactions are the so-called nonlocal models, which are the subject of this work.
The nonlocal operators considered here are integral operators with a finite range of interaction and the resulting models can be applied to anomalous diffusion, mechanics and multiscale problems.
While the range of applications is vast, the applicability of nonlocal models can face problems such as the high computational and algorithmic complexity of fundamental tasks. One of them is the assembly of finite element discretizations of truncated, nonlocal operators.
The first contribution of this thesis is therefore an openly accessible, documented Python code which allows to compute finite element approximations for nonlocal convection-diffusion problems with truncated interaction horizon.
Another difficulty in the solution of nonlocal problems is that the discrete systems may be ill-conditioned which complicates the application of iterative solvers. Thus, the second contribution of this work is the construction and study of a domain decomposition type solver that is inspired by substructuring methods for differential equations. The numerical results are based on the abstract framework of nonlocal subdivisions which is introduced here and which can serve as a guideline for general nonlocal domain decomposition methods.
We consider a linear regression model for which we assume that some of the observed variables are irrelevant for the prediction. Including the wrong variables in the statistical model can either lead to the problem of having too little information to properly estimate the statistic of interest, or having too much information and consequently describing fictitious connections. This thesis considers discrete optimization to conduct a variable selection. In light of this, the subset selection regression method is analyzed. The approach gained a lot of interest in recent years due to its promising predictive performance. A major challenge associated with the subset selection regression is the computational difficulty. In this thesis, we propose several improvements for the efficiency of the method. Novel bounds on the coefficients of the subset selection regression are developed, which help to tighten the relaxation of the associated mixed-integer program, which relies on a Big-M formulation. Moreover, a novel mixed-integer linear formulation for the subset selection regression based on a bilevel optimization reformulation is proposed. Finally, it is shown that the perspective formulation of the subset selection regression is equivalent to a state-of-the-art binary formulation. We use this insight to develop novel bounds for the subset selection regression problem, which show to be highly effective in combination with the proposed linear formulation.
In the second part of this thesis, we examine the statistical conception of the subset selection regression and conclude that it is misaligned with its intention. The subset selection regression uses the training error to decide on which variables to select. The approach conducts the validation on the training data, which oftentimes is not a good estimate of the prediction error. Hence, it requires a predetermined cardinality bound. Instead, we propose to select variables with respect to the cross-validation value. The process is formulated as a mixed-integer program with the sparsity becoming subject of the optimization. Usually, a cross-validation is used to select the best model out of a few options. With the proposed program the best model out of all possible models is selected. Since the cross-validation is a much better estimate of the prediction error, the model can select the best sparsity itself.
The thesis is concluded with an extensive simulation study which provides evidence that discrete optimization can be used to produce highly valuable predictive models with the cross-validation subset selection regression almost always producing the best results.