TY - THES A1 - Michel, René T1 - Simulation and Estimation in Multivariate Generalized Pareto Models T1 - Simulationen und Schätzverfahren in multivariaten verallgemeinerten Pareto-Modellen N2 - The investigation of multivariate generalized Pareto distributions (GPDs) in the framework of extreme value theory has begun only lately. Recent results show that they can, as in the univariate case, be used in Peaks over Threshold approaches. In this manuscript we investigate the definition of GPDs from Section 5.1 of Falk et al. (2004), which does not differ in the area of interest from those of other authors. We first show some theoretical properties and introduce important examples of GPDs. For the further investigation of these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. This algorithm is based on the Shi transformation, which was introduced by Shi (1995) and was used in Stephenson (2003) for the simulation of multivariate extreme value distributions of logistic type. We also present nonparametric and parametric estimation methods in GPD models. We estimate the angular density nonparametrically in arbitrary dimension, where the bivariate case turns out to be a special case. The asymptotic normality of the corresponding estimators is shown. Also in the parametric estimations, which are mainly based on maximum likelihood methods, the asymptotic normality of the estimators is shown under certain regularity conditions. Finally the methods are applied to a real hydrological data set containing water discharges of the rivers Altmühl and Danube in southern Bavaria. N2 - Die Untersuchung der multivariaten verallgemeinerten Pareto-Verteilungen (GPDs) im Rahmen der Extremwerttheorie hat erst kürzlich begonnen. Neueste Ergebnisse zeigen, dass diese wie im univariaten Fall bei Peaks over Threshold-Ansätzen angewendet werden können. In dieser Arbeit verwenden wir die Definition einer GPD aus Abschnitt 5.1 von Falk et al. (2004), die sich im interessierenden Bereich nicht von der anderer Autoren unterscheidet. Wir zeigen zuerst einige theoretische Eigenschaften und stellen wichtige Beispiele von GPDs vor. Zur weiteren Untersuchung dieser Verteilungen sind Simulationen unerläßlich. Wir stellen mehrere Methoden zur Simulation von GPDs vor, beginnend mit einer effizienten Methode für die logistische GPD. Der entsprechende Algorithmus basiert auf der Shi-Transformation, die von Shi (1995) eingeführt und von Stephenson (2003) verwendet wurde, um logistische multivariate Extremwertverteilungen zu simulieren. Wir führen auch nicht-parametrische und parametrische Schätzverfahren in GPD-Modellen ein. Wir schätzen die Angular Density in beliebiger Dimension, wobei sich der bivariate Fall als ein besonderer herausstellt. Die asymptotische Normalität der entsprechenden Schätzer wird gezeigt. Ebenso zeigen wir für die parametrischen Schätzungen, die hauptsächlich Maximum-Likelihood-Methoden verwenden, die asymptotische Normalität unter geeigneten Regularitätsbedingungen Zum Schluß werden die Methoden auf einen realen hydrologischen Datensatz, bestehend aus Abflussraten der Flüsse Altmühl und Donau in Südbayern, angewendet. KW - Pareto-Verteilung KW - Multivariate verallgemeine Pareto-Verteilungen KW - Extremwerttheorie KW - Überschreitungen KW - Simulation KW - Angular Density KW - Multivariate Generalized Pareto Distributions KW - Peaks over Threshold KW - Extreme Value Theory KW - Simulation KW - Angular Density Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-18489 ER - TY - BOOK A1 - Falk, Michael A1 - Marohn, Frank A1 - Michel, René A1 - Hofmann, Daniel A1 - Macke, Maria A1 - Tewes, Bernward A1 - Dinges, Peter A1 - Spachmann, Christoph A1 - Englert, Stefan T1 - A First Course on Time Series Analysis : Examples with SAS N2 - The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS. Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License. KW - Zeitreihenanalyse KW - Box-Jenkins-Verfahren KW - SAS KW - Zustandsraummodelle KW - Time Series Analysis KW - State-Space Models KW - Frequency Domain KW - Box–Jenkins Program Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-56489 N1 - Version: 2011-March-01 ER - TY - BOOK A1 - Falk, Michael A1 - Marohn, Frank A1 - Michel, René A1 - Hofmann, Daniel A1 - Macke, Maria A1 - Tewes, Bernward A1 - Dinges, Peter T1 - A First Course on Time Series Analysis : Examples with SAS N2 - The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License. KW - Zeitreihenanalyse KW - SAS KW - Zeitreihenanalyse KW - SAS KW - Time series analyses KW - SAS Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-12593 ER - TY - BOOK A1 - Falk, Michael A1 - Marohn, Frank A1 - Michel, René A1 - Hofmann, Daniel A1 - Macke, Maria A1 - Tewes, Bernward A1 - Dinges, Peter T1 - A First Course on Time Series Analysis : Examples with SAS N2 - The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License. KW - Zeitreihenanalyse KW - SAS KW - Zeitreihenanalyse KW - SAS KW - Time series analyses KW - SAS Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-16919 ER - TY - BOOK A1 - Falk, Michael A1 - Marohn, Frank A1 - Michel, René A1 - Hofmann, Daniel A1 - Macke, Maria A1 - Spachmann, Christoph A1 - Englert, Stefan T1 - A First Course on Time Series Analysis : Examples with SAS [Version 2012.August.01] N2 - The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS. Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License. KW - Zeitreihenanalyse KW - Box-Jenkins-Verfahren KW - SAS KW - Zustandsraummodelle KW - Time Series Analysis KW - State-Space Models KW - Frequency Domain KW - Box–Jenkins Program Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-72617 N1 - Version: 2012-August-01 ER -