Mathematical Statistics E-Book

Dieter Rasch

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 874

Veröffentlichungsjahr: 2018

Beschreibung

Explores mathematical statistics in its entirety--from the fundamentals to modern methods This book introduces readers to point estimation, confidence intervals, and statistical tests. Based on the general theory of linear models, it provides an in-depth overview of the following: analysis of variance (ANOVA) for models with fixed, random, and mixed effects; regression analysis is also first presented for linear models with fixed, random, and mixed effects before being expanded to nonlinear models; statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests; and design of experiments from a mathematical-statistical point of view. Most analysis methods have been supplemented by formulae for minimal sample sizes. The chapters also contain exercises with hints for solutions. Translated from the successful German text, Mathematical Statistics requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables), which is typically taught in the earlier semesters of scientific and mathematical study courses. It teaches readers all about statistical analysis and covers the design of experiments. The book also describes optimal allocation in the chapters on regression analysis. Additionally, it features a chapter devoted solely to experimental designs. * Classroom-tested with exercises included * Practice-oriented (taken from day-to-day statistical work of the authors) * Includes further studies including design of experiments and sample sizing * Presents and uses IBM SPSS Statistics 24 for practical calculations of data Mathematical Statistics is a recommended text for advanced students and practitioners of math, probability, and statistics.

Leseprobe

Mathematical Statistics

Dieter Rasch

University of Natural Resources and Life Sciences, Institute of Applied Statistics and Computing

Vienna, Austria

Dieter Schott

Faculty of Engineering, Hochschule Wismar, University of Applied Sciences: Technology, Business and Design

Wismar, Germany

Preface

‘Mathematical statistics’ never lost its attractiveness, both as a mathematical discipline and for its applications in nearly all parts of empirical research. During the last years it was found that not everything that is mathematically optimal is also practically recommendable if we are not sure whether the assumptions (for instance, normality) are valid.

As an example we consider the two‐sample t‐test that is an optimal (uniformly most powerful unbiased) test if all assumptions are fulfilled. In applications however, we are often not sure that both variances are equal. Then the approximate Welch test is preferable. Such results have been found by extensive simulation experiments that played a much greater role the last time (see the eight international conferences about this topic since 1994 under http://iws.boku.ac.at).

Therefore we wrote in 2016 a new book in German (Rasch and Schott, 2016) based on Rasch (1995) incorporating the developments of the last years.

We dropped the first part of the book from 1995 containing measure and probability theory because we have excellent books about this such as Billingsley (2012) and Kallenberg (2002).

Considering the positive resonance to this book in the community of statistics, we decided to present an English version of our book from 2016. We thank Alison Oliver for the reception into Wiley’s publishing programme.

We assume from probability theory knowledge about exponential families as well as central and non‐central t‐, ‐ and F‐distributions. Because the definition of exponential families is basic for some chapters, it is repeated in this book.

Most of the authors of books about mathematical statistics assume that data already exist and must be analysed. But we think that the optimal design for collecting data is at least as important as the statistical analysis. Therefore, in addition to statistical analysis, we included the design of experiments. The optimal allocation is described in the chapters on regression analysis. Finally a chapter about experimental designs is added.

For practical calculations of data, we present and use in some parts of the book IBM SPSS Statistics 24 for the statistical analysis, and we thank Dr. Johannes Gladitz (Berlin) for giving us access to it. Unfortunately, it is not possible to change within SPSS to British English – therefore, you find in the screens and in our command ‘Analyze’.

The determination of sample sizes can be found together with the description of the method of analysis, and for the sample size determination and other design problems, we offer the package OPDOE (Optimal Design of Experiments) under .

We heartily thank Prof. Dr. Rob Verdooren (Wageningen, Netherlands) for proving the correctness of statistics and Sandra Almgren (Kremmling, CO, USA) for improving the English text.

Rostock, December 2017 Dieter Rasch and Dieter Schott

References

Billingsley, P. (2012)

Probability and Measure

, John Wiley & Sons, Inc., New York.

Kallenberg, O. (2002)

Foundations of Modern Probability

, 2nd edition, Springer, New York.

Rasch, D. (1995)

Mathematische Statistik

, Johann Ambrosius Barth, Berlin, Heidelberg.

Rasch, D. and Schott, D. (2016)

Mathematische Statistik

, Wiley VCH, Weinheim.