The thesis examines technical efficiency using frontier efficiency estimation techniques from parametric and non-parametric approaches. Five different frontier efficiency estimation techniques are considered which are SFA, DFA, DEA-CCR, DEA-BCC and DEA-RAM. These techniques are then used on an artificially generated panel dataset using a two-input two-output production function framework based on characteristics of German life-insurers. The key contribution of the thesis is firstly, a study that uses simulated panel dataset to estimate frontier efficiency techniques and secondly, a research framework that compares multiple frontier efficiency techniques across parametric and non-parametric approaches in the context of simulated panel data. The findings suggest that, as opposed to previous studies, parametric and non-parametric approaches can both generate comparable technical efficiency scores with simulated data. Moreover, techniques from parametric approaches, i.e. SFA and DFA are consistent with each other whereas the same applies to non-parametric approaches, i.e. DEA models. The research study also discusses some important theoretical and methodological implication of the findings and suggests some ways whereby future research can enable to overcome some of the restrictions associated with current approaches.

The k-sample data setting is one of the most common data settings used today. The null hypothesis that is most generally of interest for these methods is that the k-samples have the same location. Currently there are several procedures available for the individual who has data of this type. The most often used method is commonly called the ANOVA F-test. This test assumes that all of the underlying distributions are normal, with equal variances. Thus the only allowable difference in the distributions is a possible shift, under the alternative hypothesis. Under the null hypothesis, it is assumed that all k distributions are identical, not just equally located. Current nonparametric methods for the k-sample setting require a variety of restrictions on the distribution of the data. The most commonly used method is that due to Kruskal and Wallis (1952). The method, commonly called the Kruskal-Wallis test, does not assume that the data come from normal populations, though they must still be continuous, but maintains the requirement that the populations must be identical under the null, and may differ only by a possible shift under the alternative. In this work a new procedure is developed which is exactly distribution free when the distributions are equivalent and continuous under the null hypothesis, and simulations are used to study the properties of the test when the distributions are continuous and have the same medians under the null. The power of the statistic under alternatives is also studied. The test bears a resemblance to the two sample sign type tests, which will be pointed out as the development is shown. / Ph. D.

Ce travail est consacré au problème de construction des tests d'ajustement dans le cas des processus stochastiques observés en temps continu. Comme modèles d'observations, nous considérons les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. Sous l'hypothèse nulle, nous traitons le cas où chaque modèle dépend d'un paramètre inconnu unidimensionnel et nous proposons l'estimateur de distance minimale pour ce paramètre. Notre but est la construction des tests d'ajustement « asymptotically distribution free » (ADF) de niveau asymtotique α ϵ (0,1) dans le cas de cette hypothèse paramétrique pour les modèles traités. Nous montrons alors que la limite de chaque statistique étudiée ne dépend ni du modèle ni du paramètre inconnu. Les tests d'ajustement basés sur ces statistiques sont donc ADF. L'objectif principal de ce travail est la construction d'une transformation linéaire spéciale. En particulier, nous résolvons l'équation de Fredholm du second type avec le noyau dégénéré. Sa solution nous permet de construire la transformation linéaire désirée. Ensuite, nous montrons que l'application de cette transformation aux statistiques de base étudiées dans chaque modèle nous aide à introduire des statistiques ayant la même limite (l'intégrale du carrée du processus de Wiener). Cette dernière est « distribution free » vu qu'elle ne dépend ni du modèle ni du paramètre inconnu. Par conséquent, nous proposons des tests d'ajustement ADF en se basant sur cette transformation linéaire pour les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. / This work is devoted to the problem of the construction of several goodness of-fit (GoF) tests in the case of somestochastic processes observed in continuous time. As models of observations, we take "small noise" and ergodic diffusionprocesses and an inhomogeneous Poisson process. Under the null hypothesis, we treat the case where each model depends on an unknown one-dimensional parameter and we consider the minimum distance estimator for this parameter. Our goal is to propose "asymptotically distribution free" (ADF) GoF tests of asymptotic size α ϵ (0,1) in the case of the parametric null hypotheses for the considered models. Indeed, we show that the limit of each studied statistic does not depend on the model and the unknown parameter. Therefore, the tests based on these statistics are ADF.The main purpose of this work is to construct a special linear transformation. In particular, we solve Fredholm equation ofthe second kind with degenerated kernel. Its solution gives us the desired linear transformation. Next, we show that theapplication of this transformation to the basic statistics allows us to introduce statistics with the same limit (the integral of the square of the Wiener process). The latter is "distribution free" because it does not depend on the models and the unknown parameter. Therefore, we construct the ADF GoF tests which are based on this linear transformation for the diffusion ("small noise" and ergodic) and inhomogeneous Poisson processes.

Real-life transportation systems are subject to numerous uncertainties in their operation. Researchers have suggested various reliability measures to characterize their network-level performances. One of these measures is given by travel time reliability, defined as the probability that travel times remain below certain (acceptable) levels. Existing reliability assessment (and optimization) techniques tend to be computationally intensive. In this dissertation we develop computationally efficient alternatives. In particular, we make the following three contributions. In the first contribution, we present a novel reliability assessment methodology when the source of uncertainty is given by road capacities. More specifically, we present a method based on the theory of Fourier transforms to numerically approximate the probability density function of the (system-wide) travel time. The proposed methodology takes advantage of the established computational efficiency of the fast Fourier transform. In the second contribution, we relax the common assumption that probability distributions of the sources of uncertainties are known explicitly. In reality, this distribution may be unavailable (or inaccurate) as we may have no (or insufficient) data to calibrate the distributions. We present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is any positive integer) of the travel time to be known and that the travel times reside in a set of known and bounded intervals. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop analytical probability inequalities to quickly obtain upper bounds on the desired probability. Because of the computationally intensive nature of (virtually all) existing reliability assessment techniques, the optimization of the reliability of transportation systems has generally been computationally prohibitive. The third and final contribution of this dissertation is the introduction of a new transportation network design model in which the objective is to minimize the unreliability of travel time. The computational requirements are shown to be much lower due to the assessment techniques developed in this dissertation. Moreover, numerical results suggest that it has the potential to form a computationally efficient proxy for current simulation-based network design models. / text

Developing nonparametric statistical methods and inference procedures for high-dimensional large data have been a challenging frontier problem of statistics. To attack this problem, in recent years, a clear rising trend has been observed with a radically different viewpoint--``Graph-based Nonparametrics," which is the main research focus of this dissertation. The basic idea consists of two steps: (i) representation step: code the given data using graphs, (ii) analysis step: apply statistical methods on the graph-transformed problem to systematically tackle various types of data structures. Under this general framework, this dissertation develops two major research directions. Chapter 2—based on Mukhopadhyay and Wang (2019a)—introduces a new nonparametric method for high-dimensional k-sample comparison problem that is distribution-free, robust, and continues to work even when the dimension of the data is larger than the sample size. The proposed theory is based on modern LP-nonparametrics tools and unexplored connections with spectral graph theory. The key is to construct a specially-designed weighted graph from the data and to reformulate the k-sample problem into a community detection problem. The procedure is shown to possess various desirable properties along with a characteristic exploratory flavor that has practical consequences. The numerical examples show surprisingly well performance of our method under a broad range of realistic situations. Chapter 3—based on Mukhopadhyay and Wang (2019b)—revisits some foundational questions about network modeling that are still unsolved. In particular, we present unified statistical theory of the fundamental spectral graph methods (e.g., Laplacian, Modularity, Diffusion map, regularized Laplacian, Google PageRank model), which are often viewed as spectral heuristic-based empirical mystery facts. Despite half a century of research, this question has been one of the most formidable open issues, if not the core problem in modern network science. Our approach integrates modern nonparametric statistics, mathematical approximation theory (of integral equations), and computational harmonic analysis in a novel way to develop a theory that unifies and generalizes the existing paradigm. From a practical standpoint, it is shown that this perspective can provide adequate guidance for designing next-generation computational tools for large-scale problems. As an example, we have described the high-dimensional change-point detection problem. Chapter 4 discusses some further extensions and application of our methodologies to regularized spectral clustering and spatial graph regression problems. The dissertation concludes with the a discussion of two important areas of future studies. / Statistics

<p>In statistical inference of the distribution-free straight-line regression problem, two common transformations, rank transformation and sign transformation, are used to construct the test statistics. When shall we need to use the transformations and which transformation is more efficient are two common questions met by researchers. In this thesis, we will discuss the comparison of the efficiencies of the statistics before and after the rank transformation or the sign transformation in both theoretical and practical ways. Simulation is also used to compare the efficiencies of the statistics under different distributions. Some recommendations about when to use transformations and which one to choose are put forward associated with the conclusion drawn from the research work we have done.</p>

In statistical inference of the distribution-free straight-line regression problem, two common transformations, rank transformation and sign transformation, are used to construct the test statistics. When shall we need to use the transformations and which transformation is more efficient are two common questions met by researchers. In this thesis, we will discuss the comparison of the efficiencies of the statistics before and after the rank transformation or the sign transformation in both theoretical and practical ways. Simulation is also used to compare the efficiencies of the statistics under different distributions. Some recommendations about when to use transformations and which one to choose are put forward associated with the conclusion drawn from the research work we have done.

Statistical process control (SPC) is a toolbox to detect changes in the output of a process distribution. It can serve as a valuable resource to maintain high quality in a manufacturing process. This report is based on the work on evaluating and implementing methods for SPC in the process of chromatography instrument manufacturing at GE Healthcare, Umeå. To handle low volume and non-normally distributed process output data, non-parametric methods are considered. Eight control charts, three for for Phase I analysis, and five for Phase II analysis, are evaluated in this study. The usability of the charts are assessed based on ease of interpretation and the performance to detect distributional changes. The later is evaluated with simulations. The result of the project is the implementation of the RS/P-chart, suggested by Capizzi et al (2013), for Phase I analysis. Of the considered Phase I methods (and simulation scenarios), the RS/P-chart has the highest overall probability, of detecting a variety of distributional changes. Further, the RS/P-chart is easily interpreted, facilitating the analysis. For Phase II analysis, the use of two control charts, one based on the Mann-Whitney U statistic, suggested by Chakraborti et al (2008), and one on the Mood test statistic for dispersion, suggested by Ghute et al (2014), have been implemented. These are chosen mainly based on the ease of interpretation. To reduce the detection time for changes in the process distribution, the change-point chart based on the Cramer Von Mises statistic, suggested by Ross et al (2012), could be used instead. Using single observations, instead of larger samples, this chart is updated more frequently. However, this efficiently increases the false alarm rate and the chart is also considered much more difficult to interpret for the SPC practitioner. / Statistisk processkontroll (SPC) är en samling verktyg för att upptäcka förändringar, i fördelningen, hos utfallen i en process. Det kan fungera som en värdefull resurs för att upprätthålla en hög kvalitet i en tillverkningsprocess. Denna rapport är baserad på arbetet med att utvärdera och implementera metoder för SPC i en monteringsprocess av kromatografiinstrument på GE Healthcare, Umeå. Åtta styrdiagram, tre för för fas I analys, och fem för fas II analys, studeras i denna rapport. Användbarheten hos styrdiagrammen bedöms efter hur enkla de är att tolka och förmågan att upptäcka fördelningsförändringar. Den senare utvärderas med simuleringar. Resultatet av projektet är införandet av RS/P-metod, utvecklad av Capizzi et al (2013), för analysen i fas I. Av de utvärderade metoderna, (och simuleringsscenarier), har RS/P-diagrammet den högsta övergripande sannolikheten, för att upptäcka en mängd olika fördelningsförändringar. Vidare är metodens grafiska diagram lätt att tolka, vilket underlättar analysen. För fas II analys, har två styrdiagram, ett baserat på Mann-Whitney's U teststatistika, som föreslagits av Chakraborti et al (2008), och ett på Mood's teststatistika för spridning, som föreslagits av Ghute et al (2014), implementerats. Styrkan i dessa styrdiagram ligger främst i dess enkla tolkning. För snabbare identifiering av processförändringar kan styrdiagrammet baserat på Cramer von Mises teststatistika, som föreslagits av Ross et al (2012), användas. Baserat på enskilda observationer, istället för stickprov, har styrdiagrammet en högre uppdateringsfrekvens. Detta leder dock till ett ökat antal falska larm och styrdiagrammet anses dessutom vara avsevärt mycket svårare att tolka för SPC-utövaren.

This diploma thesis deals with the new trends in the monetization of the video gaming industry with emphasis on crowdfunding, free-to-play model, selling games by "pay what you want" bundles and sales on Steam and other digital distribution stores. The purpose of this diploma thesis is to describe how the players on personal computers react to these trends in the Czech Republic. First, the situation in Czech gaming industry and the situation of players in the Czech Republic is described. Then, the new trends are analyzed thoroughly using foreign researches. The practical part analyses the effects of the new trends on Czech players with the results of an online questionnaire. First, the methodology is presented and subsequently the collected data is analyzed. Gradually, the thesis are answering the three research questions which are clarifying various aspects of how the Czech players respond to the new trends in the video gaming industry monetization. Powered by TCPDF (www.tcpdf.org)

<p dir="ltr">Differential privacy (DP) uses a probabilistic framework to measure the level of privacy protection of a mechanism that releases data analysis results to the public. Although DP is widely used by both government and industry, there is still a lack of research on statistical inference under DP guarantees. On the one hand, existing DP mechanisms mainly aim to extract dataset-level information instead of population-level information. On the other hand, DP mechanisms introduce calibrated noises into the released statistics, which often results in sampling distributions more complex and intractable than the non-private ones. This dissertation aims to provide general-purpose methods for statistical inference, such as confidence intervals (CIs) and hypothesis tests (HTs), that satisfy the DP guarantees. </p><p dir="ltr">In the first part of the dissertation, we examine a DP bootstrap procedure that releases multiple private bootstrap estimates to construct DP CIs. We present new DP guarantees for this procedure and propose to use deconvolution with DP bootstrap estimates to derive CIs for inference tasks such as population mean, logistic regression, and quantile regression. Our method achieves the nominal coverage level in both simulations and real-world experiments and offers the first approach to private inference for quantile regression.</p><p dir="ltr">In the second part of the dissertation, we propose to use the simulation-based ``repro sample'' approach to produce CIs and HTs based on DP statistics. Our methodology has finite-sample guarantees and can be applied to a wide variety of private inference problems. It appropriately accounts for biases introduced by DP mechanisms (such as by clamping) and improves over other state-of-the-art inference methods in terms of the coverage and type I error of the private inference. </p><p dir="ltr">In the third part of the dissertation, we design a debiased parametric bootstrap framework for DP statistical inference. We propose the adaptive indirect estimator, a novel simulation-based estimator that is consistent and corrects the clamping bias in the DP mechanisms. We also prove that our estimator has the optimal asymptotic variance among all well-behaved consistent estimators, and the parametric bootstrap results based on our estimator are consistent. Simulation studies show that our framework produces valid DP CIs and HTs in finite sample settings, and it is more efficient than other state-of-the-art methods.</p>