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O Supremo Tribunal Federal (STF) é uma das instituições mais importantes do país, e tem recebido cada vez mais atenção da sociedade brasileira. Ano a ano, a corte é acionada para julgar dezenas de milhares de casos, muitos deles com impacto direto na vida econômica, política e social do país. Investigar quais são os fatores que influenciam o comportamento dos ministros do STF é fundamental para compreendermos o processo de tomada de decisões do Tribunal. Apesar de existirem estudos importantes sobre o resultado das ações de controle de constitucionalidade, ainda existe espaço para estudar o comportamento individual dos ministros. O objetivo do presente trabalho é analisar o comportamento individual dos ministros do STF, utilizando-se as votações dos ministros frente às ações de controle de constitucionalidade que foram decididas de forma colegiada. A proposta de trabalho é verificar como os ministros se agrupam e quais fatores influenciam sua divisão. Para isso, propomos a utilização do método de estimação de pontos ideias. Nossa hipótese primária de trabalho é que existe uma influência da indicação presidencial no comportamento dos ministros do Supremo Tribunal Federal. Dessa forma, haveria uma divisão da Corte entre os ministros nomeados por diferentes partidos. A hipótese secundária seria que as trajetórias profissionais dos ministros também influenciam em sua forma de decidir, sendo possível, portanto, identificar divisões entre os ministros a partir desta variável. Os resultados do presente trabalho indicam que variáveis associadas aos modelos atitudinais do comportamento judicial, partidos dos presidentes que indicaram os ministros, ideologia e filosofia judicial dos ministros, são variáveis mais relevantes para explicar as agrupamentos e dissensos no STF do que as que dizem respeito as trajetórias profissionais dos juízes. / The Supremo Tribunal Federal - STF (Federal Supreme Court) is one of the most relevant institutions in Brazil, and it has increasingly gained attention from Brazilian society. Year after year, the Court is demanded to rule thousands of cases, a lot of them with direct impact in the countrys economic political and social life. To investigate which factors influence the Justices behavior is paramount to understand the decision-making process of the Court. The goal of this work is to analyze the Justices individual behavior, by looking at the Justices individual vote in Constitutional Review cases that were decided in collegiate manner. This dissertation verifies how the Justices cluster themselves and which factors influence their division. For that, we employ the ideal point estimation method. Our primary hypothesis states that the presidential nomination exerts influence in the Justices behavior. In this way, it would be possible to identify a division in the Court among Justices nominated by different parties. Our secondary hypothesis states that the Justices professional background also exerts influence in how they decide, therefore making possible to identify divisions among Justices by taking this variable as a dividing line. The results of the present work indicate that the variables associated with the attitudinal models of judicial behavior, presidential party responsible for Justice nomination, ideology and Justices judicial philosophy are more relevant variables to explain the clusters and dissensus in STF than variables linked to magistrates professional background.

O Supremo Tribunal Federal (STF) é uma das instituições mais importantes do país, e tem recebido cada vez mais atenção da sociedade brasileira. Ano a ano, a corte é acionada para julgar dezenas de milhares de casos, muitos deles com impacto direto na vida econômica, política e social do país. Investigar quais são os fatores que influenciam o comportamento dos ministros do STF é fundamental para compreendermos o processo de tomada de decisões do Tribunal. Apesar de existirem estudos importantes sobre o resultado das ações de controle de constitucionalidade, ainda existe espaço para estudar o comportamento individual dos ministros. O objetivo do presente trabalho é analisar o comportamento individual dos ministros do STF, utilizando-se as votações dos ministros frente às ações de controle de constitucionalidade que foram decididas de forma colegiada. A proposta de trabalho é verificar como os ministros se agrupam e quais fatores influenciam sua divisão. Para isso, propomos a utilização do método de estimação de pontos ideias. Nossa hipótese primária de trabalho é que existe uma influência da indicação presidencial no comportamento dos ministros do Supremo Tribunal Federal. Dessa forma, haveria uma divisão da Corte entre os ministros nomeados por diferentes partidos. A hipótese secundária seria que as trajetórias profissionais dos ministros também influenciam em sua forma de decidir, sendo possível, portanto, identificar divisões entre os ministros a partir desta variável. Os resultados do presente trabalho indicam que variáveis associadas aos modelos atitudinais do comportamento judicial, partidos dos presidentes que indicaram os ministros, ideologia e filosofia judicial dos ministros, são variáveis mais relevantes para explicar as agrupamentos e dissensos no STF do que as que dizem respeito as trajetórias profissionais dos juízes. / The Supremo Tribunal Federal - STF (Federal Supreme Court) is one of the most relevant institutions in Brazil, and it has increasingly gained attention from Brazilian society. Year after year, the Court is demanded to rule thousands of cases, a lot of them with direct impact in the countrys economic political and social life. To investigate which factors influence the Justices behavior is paramount to understand the decision-making process of the Court. The goal of this work is to analyze the Justices individual behavior, by looking at the Justices individual vote in Constitutional Review cases that were decided in collegiate manner. This dissertation verifies how the Justices cluster themselves and which factors influence their division. For that, we employ the ideal point estimation method. Our primary hypothesis states that the presidential nomination exerts influence in the Justices behavior. In this way, it would be possible to identify a division in the Court among Justices nominated by different parties. Our secondary hypothesis states that the Justices professional background also exerts influence in how they decide, therefore making possible to identify divisions among Justices by taking this variable as a dividing line. The results of the present work indicate that the variables associated with the attitudinal models of judicial behavior, presidential party responsible for Justice nomination, ideology and Justices judicial philosophy are more relevant variables to explain the clusters and dissensus in STF than variables linked to magistrates professional background.

Ratingsysteme sind ein zentraler Bestandteil der Kreditrisikomodellierung. Neben der Bonitätsbeurteilung auf der Ebene der Kreditnehmer und der Risikoquantifizierung auf der Ebene der Ratingklassen spielt dabei die Bildung der Ratingklassen eine wesentliche Rolle. Die Literatur zur Ratingklassenbildung setzt auf modellfreie, in gewisser Weise willkürliche Optimierungsverfahren. Ein Ziel der vorliegenden Arbeit ist es, stattdessen ein parametrisches statistisches Modell zur Bildung der Ratingklassen einzuführen. Ein geeignetes Modell ist im Bereich der Bruchpunktschätzung zu finden. Dieses Modell und die in der mathematischen Literatur vorgeschlagenen Parameter- und Intervallschätzer werden in der vorliegenden Arbeit dargestellt und gründlich diskutiert. Dabei wird Wert auf eine anwendungsnahe und anschauliche Formulierung der mathematisch-statistischen Sachverhalte gelegt. Anschließend wird die Methodik der Bruchpunktschätzung auf einen konkreten Datensatz angewendet und mit verschiedenen anderen Kriterien zur Ratingklassenbildung verglichen. Hier erweist sich die Bruchpunktschätzung als vorteilhaft. Aufbauend auf der empirischen Untersuchung wird abschließend weiterer Forschungsbedarf abgeleitet. Dazu werden insbesondere Konzepte für den Mehrklassenfall und für abhängige Daten entworfen. / Rating systems are a key component of credit risk modeling. In addition to scoring at borrowers’ level and risk quantification at the level of rating classes, the formation of the rating classes plays a fundamental role. The literature on rating classification uses in a way arbitrary optimization methods. Therefore, one aim of this contribution is to introduce a parametric statistical model to form the rating classes. A suitable model can be found in the area of split-point estimation. This model and the proposed parameter and interval estimators are presented and thoroughly discussed. Here, emphasis is placed on an application-oriented and intuitive formulation of the mathematical and statistical issues. Subsequently, the methodology of split-point estimation is applied to a specific data set and compared with several other criteria for rating classification. Here, split-point estimation proves to be advantageous. Finally, further research questions are derived on the basis of the empirical study. In particular, concepts for the case of more than two classes and for dependent data are sketched.

The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.

Ratingsysteme sind ein zentraler Bestandteil der Kreditrisikomodellierung. Neben der Bonitätsbeurteilung auf der Ebene der Kreditnehmer und der Risikoquantifizierung auf der Ebene der Ratingklassen spielt dabei die Bildung der Ratingklassen eine wesentliche Rolle. Die Literatur zur Ratingklassenbildung setzt auf modellfreie, in gewisser Weise willkürliche Optimierungsverfahren. Ein Ziel der vorliegenden Arbeit ist es, stattdessen ein parametrisches statistisches Modell zur Bildung der Ratingklassen einzuführen. Ein geeignetes Modell ist im Bereich der Bruchpunktschätzung zu finden. Dieses Modell und die in der mathematischen Literatur vorgeschlagenen Parameter- und Intervallschätzer werden in der vorliegenden Arbeit dargestellt und gründlich diskutiert. Dabei wird Wert auf eine anwendungsnahe und anschauliche Formulierung der mathematisch-statistischen Sachverhalte gelegt. Anschließend wird die Methodik der Bruchpunktschätzung auf einen konkreten Datensatz angewendet und mit verschiedenen anderen Kriterien zur Ratingklassenbildung verglichen. Hier erweist sich die Bruchpunktschätzung als vorteilhaft. Aufbauend auf der empirischen Untersuchung wird abschließend weiterer Forschungsbedarf abgeleitet. Dazu werden insbesondere Konzepte für den Mehrklassenfall und für abhängige Daten entworfen.:1. Einleitung 2. Ratingsystem 3. Bruchpunktschätzung 4. Anwendung 5. Zusammenfassung und Ausblick / Rating systems are a key component of credit risk modeling. In addition to scoring at borrowers’ level and risk quantification at the level of rating classes, the formation of the rating classes plays a fundamental role. The literature on rating classification uses in a way arbitrary optimization methods. Therefore, one aim of this contribution is to introduce a parametric statistical model to form the rating classes. A suitable model can be found in the area of split-point estimation. This model and the proposed parameter and interval estimators are presented and thoroughly discussed. Here, emphasis is placed on an application-oriented and intuitive formulation of the mathematical and statistical issues. Subsequently, the methodology of split-point estimation is applied to a specific data set and compared with several other criteria for rating classification. Here, split-point estimation proves to be advantageous. Finally, further research questions are derived on the basis of the empirical study. In particular, concepts for the case of more than two classes and for dependent data are sketched.:1. Einleitung 2. Ratingsystem 3. Bruchpunktschätzung 4. Anwendung 5. Zusammenfassung und Ausblick

This thesis investigates some problems related to the form and shape of statistical distributions with the main focus on goodness of fit and bump hunting. A bump is a distinctive characteristic of distributional shape. A search for bumps, or bump hunting, in a probability density function (PDF) has long been an important topic in statistical research. We introduce a new definition of a bump which relies on the notion of the curvature of a planar curve. We then propose a new method for bump hunting which is based on a kernel density estimator of the unknown PDF. The method gives not only the number of bumps but also the location of their centers and base points. In quantitative risk applications, the selection of distributions that properly capture upper tail behavior is essential for accurate modeling. We study tests of distributional form, or goodness-of-fit (GoF) tests, that assess simple hypotheses, i.e., when the parameters of the hypothesized distribution are completely specified. From theoretical and practical perspectives, we analyze the limiting properties of a family of weighted Cramér-von Mises GoF statistics W2 with weight function psi(t)=1/(1-t)^beta (for beta<=2) which focus on the upper tail. We demonstrate that W2 has no limiting distribution. For this reason, we provide a normalization of W2 that leads to a non-degenerate limiting distribution. Further, we study W2 for composite hypotheses, i.e., when distributional parameters must be estimated from a sample at hand. When the hypothesized distribution is heavy-tailed, we examine the finite sample properties of W2 under the Chen-Balakrishnan transformation that reduces the original GoF test (the direct test) to a test for normality (the indirect test). In particular, we compare the statistical level and power of the pairs of direct and indirect tests. We observe that decisions made by the direct and indirect tests agree well, and in many cases they become independent as sample size grows. / Thesis / Doctor of Philosophy (PhD)

In the recent years, the internet has been developed rapidly. By this convenient medium, the information can be spread easily all over the world. Using the convenience and variety of internet, e-learning has become a burgeoning and efficient way for learning. The main idea of e-learning is applying the concept of Asynchronous Course Delivery, and establishing a learning environment on the internet. With the connection between computer and the internet, user can learn more in a convenient environment. In order to apply the concept of e-learning to the course of statistics, we use the Java programming language to establish an on-line interactive environment. In addition to learn some fundamental concepts of statistics, learner can also strengthen the abilities of researching and surfing by themselves. In this paper we developed six interactive examples. Not only interpreting and illustrating, we also introduce the motive, goal, relative concepts and applications in detail for each example. Finally, we hope that user can easily learn more knowledge of statistics by this learning environment, then our e-learning to statistical education, can be achieved.

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In this thesis, we develop some inferential results for one-shot device testing data analysis. These extend and generalize existing methods in the literature. First, a competing-risk model is introduced for one-shot testing data under accelerated life-tests. One-shot devices are products which will be destroyed immediately after use. Therefore, we can observe only a binary status as data, success or failure, of such products instead of its lifetime. Many one-shot devices contain multiple components and failure of any one of them will lead to the failure of the device. Failed devices are inspected to identify the specific cause of failure. Since the exact lifetime is not observed, EM algorithm becomes a natural tool to obtain the maximum likelihood estimates of the model parameters. Here, we develop the EM algorithm for competing exponential and Weibull cases. Second, a semi-parametric approach is developed for simple one-shot device testing data. Semi-parametric estimation is a model that consists of parametric and non-parametric components. For this purpose, we only assume the hazards at different stress levels are proportional to each other, but no distributional assumption is made on the lifetimes. This provides a greater flexibility in model fitting and enables us to examine the relationship between the reliability of devices and the stress factors. Third, Bayesian inference is developed for one-shot device testing data under exponential distribution and Weibull distribution with non-constant shape parameters for competing risks. Bayesian framework provides statistical inference from another perspective. It assumes the model parameters to be random and then improves the inference by incorporating expert's experience as prior information. This method is shown to be very useful if we have limited failure observation wherein the maximum likelihood estimator may not exist. The thesis proceeds as follows. In Chapter 2, we assume the one-shot devices to have two components with lifetimes having exponential distributions with multiple stress factors. We then develop an EM algorithm for developing likelihood inference for the model parameters as well as some useful reliability characteristics. In Chapter 3, we generalize to the situation when lifetimes follow a Weibull distribution with non-constant shape parameters. In Chapter 4, we propose a semi-parametric model for simple one-shot device test data based on proportional hazards model and develop associated inferential results. In Chapter 5, we consider the competing risk model with exponential lifetimes and develop inference by adopting the Bayesian approach. In Chapter 6, we generalize these results on Bayesian inference to the situation when the lifetimes have a Weibull distribution. Finally, we provide some concluding remarks and indicate some future research directions in Chapter 7. / Thesis / Doctor of Philosophy (PhD)