Ludwig Fahrmeir

Dieses Lehrbuch liefert eine umfassende Darstellung der deskriptiven und induktiven Statistik sowie moderner Methoden der explorativen Datenanalyse. Dabei stehen inhaltliche Motivation, Interpretation und Verständnis der Methoden im Vordergrund. Unterstützt werden diese durch zahlreiche Grafiken und Anwendungsbeispiele, die auf realen Daten basieren, sowie passende exemplarische R-Codes und Datensätze. Die im Buch beschriebenen Ergebnisse können außerdem anhand der online zur Verfügung stehenden Materialien reproduziert sowie um eigene Analysen ergänzt werden. Eine kurze Einführung in die freie Programmiersprache R ist ebenfalls enthalten. Hervorhebungen erhöhen die Lesbarkeit und Übersichtlichkeit. Das Buch eignet sich als vorlesungsbegleitende Lektüre, aber auch zum Selbststudium. Für die 9. Auflage wurde das Buch inhaltlich überarbeitet und ergänzt. Leserinnen und Leser erhalten nun in der Springer-Nature-Flashcards-App zusätzlich kostenfreien Zugriff auf über 100 exklusive Lernfragen, mit denen sie ihr Wissen überprüfen können.

Now in its second edition, this textbook provides an applied and unified introduction to parametric, nonparametric and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through numerous examples and case studies. The most important definitions and statements are concisely summarized in boxes, and the underlying data sets and code are available online on the book’s dedicated website. Availability of (user-friendly) software has been a major criterion for the methods selected and presented. The chapters address the classical linear model and its extensions, generalized linear models, categorical regression models, mixed models, nonparametric regression, structured additive regression, quantile regression and distributional regression models. Two appendices describe the required matrix algebra, as well as elements of probability calculus and statistical inference. In this substantially revised and updated new edition the overview on regression models has been extended, and now includes the relation between regression models and machine learning, additional details on statistical inference in structured additive regression models have been added and a completely reworked chapter augments the presentation of quantile regression with a comprehensive introduction to distributional regression models. Regularization approaches are now more extensively discussed in most chapters of the book. The book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.

Now in its second edition, this textbook provides an applied and unified introduction to parametric, nonparametric and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through numerous examples and case studies. The most important definitions and statements are concisely summarized in boxes, and the underlying data sets and code are available online on the book’s dedicated website. Availability of (user-friendly) software has been a major criterion for the methods selected and presented. The chapters address the classical linear model and its extensions, generalized linear models, categorical regression models, mixed models, nonparametric regression, structured additive regression, quantile regression and distributional regression models. Two appendices describe the required matrix algebra, as well as elements of probability calculus and statistical inference. In this substantially revised and updated new edition the overview on regression models has been extended, and now includes the relation between regression models and machine learning, additional details on statistical inference in structured additive regression models have been added and a completely reworked chapter augments the presentation of quantile regression with a comprehensive introduction to distributional regression models. Regularization approaches are now more extensively discussed in most chapters of the book. The book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, matrix algebra and statistics.

The aim of this book is an applied and unified introduction into parametric, non- and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through many real data examples and case studies. Availability of (user-friendly) software has been a major criterion for the methods selected and presented. Thus, the book primarily targets an audience that includes students, teachers and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs, and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written on an intermediate mathematical level and assumes only knowledge of basic probability, calculus, and statistics. The most important definitions and statements are concisely summarized in boxes. Two appendices describe required matrix algebra, as well as elements of probability calculus and statistical inference.

Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) inference, as well as empirical Bayes procedures closely related to penalized likelihood estimation and mixed models, are considered here. Throughout, the focus is on semiparametric regression and smoothing based on basis expansions of unknown functions and effects in combination with smoothness priors for the basis coefficients. Beginning with a review of basic methods for smoothing and mixed models, longitudinal data, spatial data and event history data are treated in separate chapters. Worked examples from various fields such as forestry, development economics, medicine and marketing are used to illustrate the statistical methods covered in this book. Most of these examples have been analysed using implementations in the Bayesian software, BayesX, and some with R Codes. These, as well as some of the data sets, are made publicly available on the website accompanying this book.

Since our first edition of this book, many developments in statistical mod­ elling based on generalized linear models have been published, and our primary aim is to bring the book up to date. Naturally, the choice of these recent developments reflects our own teaching and research interests. The new organization parallels that of the first edition. We try to motiv­ ate and illustrate concepts with examples using real data, and most data sets are available on http:/ fwww. stat. uni-muenchen. de/welcome_e. html, with a link to data archive. We could not treat all recent developments in the main text, and in such cases we point to references at the end of each chapter. Many changes will be found in several sections, especially with those connected to Bayesian concepts. For example, the treatment of marginal models in Chapter 3 is now current and state-of-the-art. The coverage of nonparametric and semiparametric generalized regression in Chapter 5 is completely rewritten with a shift of emphasis to linear bases, as well as new sections on local smoothing approaches and Bayesian inference. Chapter 6 now incorporates developments in parametric modelling of both time series and longitudinal data. Additionally, random effect models in Chapter 7 now cover nonparametric maximum likelihood and a new section on fully Bayesian approaches. The modifications and extensions in Chapter 8 reflect the rapid development in state space and hidden Markov models.

In dieser Einführung werden erstmals klassische Regressionsansätze und moderne nicht- und semiparametrische Methoden in einer integrierten, einheitlichen und anwendungsorientierten Form beschrieben. Die Darstellung wendet sich an Studierende der Statistik in Wahl- und Hauptfach sowie an empirisch-statistisch und interdisziplinär arbeitende Wissenschaftler und Praktiker, zum Beispiel in Wirtschafts- und Sozialwissenschaften, Bioinformatik, Biostatistik, Ökonometrie, Epidemiologie. Die praktische Anwendung der vorgestellten Konzepte und Methoden wird anhand ausführlich vorgestellter Fallstudien demonstriert, um dem Leser die Analyse eigener Fragestellungen zu ermöglichen.

Dieses Arbeitsbuch ergänzt perfekt das Lehrbuch Fahrmeir/Künstler/Pigeot/Tutz: Statistik - Der Weg zur Datenanalyse. Es bietet eine Fülle von Aufgaben inklusive Lösungen und Computerübungen mit realen Daten. Es dient damit der Vertiefung und der Einübung des im Lehrbuch vermittelten Stoffes zur Wahrscheinlichkeitsrechnung, deskriptiven und induktiven Statistik. Die 5. Auflage enthält eine Reihe neuer Aufgaben, die hauptsächlich in Klausuren verwendet wurden.

Jeder Kredit birgt für den Kreditgeber ein Risiko, da es unsicher ist, ob der Kreditnehmer seinen Zahlungsverpflichtungen nachkommen wird. Kreditrisiken werden mit Hilfe statistischer Methoden und mathematischer Modelle gemessen. Nicht zuletzt vor dem Hintergrund Basel II hat die quantitative Kreditrisikomessung in den letzten Jahren enorm an Bedeutung gewonnen. Dieses Buch schließt die Lücke zwischen statistischer Grundlagenliteratur und mathematisch anspruchsvollen Werken zur Modellierung von Kreditrisiken. Es bietet einen Einstieg in die Kreditrisikomessung und die dafür notwendige Statistik. Ausgehend von den wichtigsten Begriffen zum Kreditrisiko werden deren statistische Analoga beschrieben. Das Buch stellt die relevanten statistischen Verteilungen dar und gibt eine Einführung in stochastische Prozesse, Portfoliomodelle und Score- bzw. Ratingmodelle. Mit zahlreichen praxisnahen Beispielen ist es der ideale Einstieg in die Kreditrisikomessung für Praktiker und Quereinsteiger.

This text is aimed at applied statisticians, graduate students of statistics, and students and researchers with a strong interest in statistics and data analysis. This second edition is extensively revised, especially those sections relating with Bayesian concepts.