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Despite significant advances in terms of the adoption of formal Intellectual Property Rights (IPR) protection, enforcement of and compliance with IPR regulations remains a contested issue in one of the world's major contemporary economies—China. The present review seeks to offer insights into possible reasons for this discrepancy as well as possible paths of future development by reviewing prior literature on IPR in China. Specifically, it focuses on the public's perspective, which is a crucial determinant of the effectiveness of any IPR regime. It uncovers possible differences with public perspectives in other countries and points to mechanisms (e.g., political, economic, cultural, and institutional) that may foster transitions over time in both formal IPR regulation and in the public perception of and compliance with IPR in China. On this basis, the review advances suggestions for future research in order to improve scholars' understanding of the public's perspective of IPR in China, its antecedents and implications.
Institutional and cultural determinants of speed of government responses during COVID-19 pandemic
(2021)
This article examines institutional and cultural determinants of the speed of government responses during the COVID-19 pandemic. We define the speed as the marginal rate of stringency index change. Based on cross-country data, we find that collectivism is associated with higher speed of government response. We also find a moderating role of trust in government, i.e., the association of individualism-collectivism on speed is stronger in countries with higher levels of trust in government. We do not find significant predictive power of democracy, media freedom and power distance on the speed of government responses.
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
The Eurosystem's Household Finance and Consumption Survey (HFCS) collects micro data on private households' balance sheets, income and consumption. It is a stylised fact that wealth is unequally distributed and that the wealthiest own a large share of total wealth. For sample surveys which aim at measuring wealth and its distribution, this is a considerable problem. To overcome it, some of the country surveys under the HFCS umbrella try to sample a disproportionately large share of households that are likely to be wealthy, a technique referred to as oversampling. Ignoring such types of complex survey designs in the estimation of regression models can lead to severe problems. This thesis first illustrates such problems using data from the first wave of the HFCS and canonical regression models from the field of household finance and gives a first guideline for HFCS data users regarding the use of replicate weight sets for variance estimation using a variant of the bootstrap. A further investigation of the issue necessitates a design-based Monte Carlo simulation study. To this end, the already existing large close-to-reality synthetic simulation population AMELIA is extended with synthetic wealth data. We discuss different approaches to the generation of synthetic micro data in the context of the extension of a synthetic simulation population that was originally based on a different data source. We propose an additional approach that is suitable for the generation of highly skewed synthetic micro data in such a setting using a multiply-imputed survey data set. After a description of the survey designs employed in the first wave of the HFCS, we then construct new survey designs for AMELIA that share core features of the HFCS survey designs. A design-based Monte Carlo simulation study shows that while more conservative approaches to oversampling do not pose problems for the estimation of regression models if sampling weights are properly accounted for, the same does not necessarily hold for more extreme oversampling approaches. This issue should be further analysed in future research.
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.
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.
Our goal is to approximate energy forms on suitable fractals by discrete graph energies and certain metric measure spaces, using the notion of quasi-unitary equivalence. Quasi-unitary equivalence generalises the two concepts of unitary equivalence and norm resolvent convergence to the case of operators and energy forms defined in varying Hilbert spaces.
More precisely, we prove that the canonical sequence of discrete graph energies (associated with the fractal energy form) converges to the energy form (induced by a resistance form) on a finitely ramified fractal in the sense of quasi-unitary equivalence. Moreover, we allow a perturbation by magnetic potentials and we specify the corresponding errors.
This aforementioned approach is an approximation of the fractal from within (by an increasing sequence of finitely many points). The natural step that follows this realisation is the question whether one can also approximate fractals from outside, i.e., by a suitable sequence of shrinking supersets. We partly answer this question by restricting ourselves to a very specific structure of the approximating sets, namely so-called graph-like manifolds that respect the structure of the fractals resp. the underlying discrete graphs. Again, we show that the canonical (properly rescaled) energy forms on such a sequence of graph-like manifolds converge to the fractal energy form (in the sense of quasi-unitary equivalence).
From the quasi-unitary equivalence of energy forms, we conclude the convergence of the associated linear operators, convergence of the spectra and convergence of functions of the operators – thus essentially the same as in the case of the usual norm resolvent convergence.
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.
This thesis addresses three different topics from the fields of mathematical finance, applied probability and stochastic optimal control. Correspondingly, it is subdivided into three independent main chapters each of which approaches a mathematical problem with a suitable notion of a stochastic particle system.
In Chapter 1, we extend the branching diffusion Monte Carlo method of Henry-Labordère et. al. (2019) to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient conditions under which the branching diffusion representation solves the PDE in the viscosity sense. Our theoretical setup directly leads to a Monte Carlo algorithm, whose applicability is showcased in two stylized high-dimensional examples. As our main application, we demonstrate how our methodology can be used to value financial positions with defaultable, systemically important counterparties.
In Chapter 2, we formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous probabilistic construction of the state process. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. We state and prove a corresponding existence theorem, and we illustrate our results in three stylized application examples. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (2013) and Cecchin and Fischer (2020).
In Chapter 3, we present a heuristic approach to tackle stochastic impulse control problems in discrete time. Based on the work of Bensoussan (2008) we reformulate the classical Bellman equation of stochastic optimal control in terms of a discrete-time QVI, and we prove a corresponding verification theorem. Taking the resulting optimal impulse control as a starting point, we devise a self-learning algorithm that estimates the continuation and intervention region of such a problem. Its key features are that it explores the state space of the underlying problem by itself and successively learns the behavior of the optimally controlled state process. For illustration, we apply our algorithm to a classical example problem, and we give an outlook on open questions to be addressed in future research.
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.