Michael Falk - Böcker

This monograph compiles the contemporary knowledge about D-norms and provides an introductory tour through the essentials of multivariate extreme value theory.

Providing a new framework for understanding the contingent self, this book is of interest to scholars and students of Romantic literature, philosophy of the self and digital humanities.

Providing a new framework for understanding the contingent self, this book is of interest to scholars and students of Romantic literature, philosophy of the self and digital humanities.

Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation.Reviews of the 2nd edition:"In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field."David Stirzaker, Bulletin of the London Mathematical Society"Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook."Holger Drees, Metrika

"Statistik in Theorie und Praxis" schlägt die Brücke statistischer Theorie und realen praktischen Anwendungen. Zum einen wird Wert auf eine saubere Herleitung der gängigen statistischen Verfahren gelegt. Zum anderen beinhaltet der zweite Themenschwerpunkt reale Anwendungen der Methoden in der Praxis. Darüber hinaus werden Projekte an der Schnittstelle zwischen Schul- und Hochschulunterricht vorgestellt. Als Software dient das kostenlose Programm R mit der zugehörigen grafischen Oberfläche R-Commander; die zahlreichen Programmbeispiele ermöglichen es, die vorgestellten Themen selbst nachzuvollziehen. Für die Lektüre werden lediglich elementare Stochastik-Kenntnisse vorausgesetzt.

This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts. The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications. The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory.

The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration will certainly be part of a future professional work of many students in mathematics or mathematical statistics. Commonly there is no natural place in a traditional curriculum for mathematics or statistics, where a bridge between theory and practice fits into. On the other hand, the demand for an education designed to supplement theoretical training by practical experience has been rapidly increasing. There exists, consequently, a bit of a dichotomy between theoretical and applied statistics, and this book tries to straddle that gap. It links up the theory of a selection of statistical procedures used in general practice with their application to real world data sets using the statistical software package SAS (Statistical Analysis System). These applications are intended to illustrate the theory and to provide, simultaneously, the ability to use the knowledge effectively and readily in execution. An introduction to SAS is given in an appendix of the book.Eight chapters present theory, sample data and SAS realization to topics such as regression analysis, categorial data analysis, analysis of variance, discriminant analysis, cluster analysis and principal components. SAS programs and data used in the book can be downloaded from the WWW page http://statistics-with-sas.ku-eichstaett.de