Mathematical Statistics

Dieter Rasch, Dieter Schott

• Publisher: Wiley
• Year: 2018
• ISBN:
  9781119385233
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Title Page
• Table of Contents
• Preface
• 1 Basic Ideas of Mathematical Statistics
• 2 Point Estimation
• 3 Statistical Tests and Confidence Estimations
• 4 Linear Models – General Theory
• 5 Analysis of Variance (ANOVA) – Fixed Effects Models (Model I of Analysis of Variance)
• 6 Analysis of Variance: Estimation of Variance Components (Model II of the Analysis of Variance)
• 7 Analysis of Variance – Models with Finite Level Populations and Mixed Models
• 8 Regression Analysis – Linear Models with Non-random Regressors (Model I of Regression Analysis) and with Random Regressors (Model II of Regression Analysis)
• 9 Regression Analysis – Intrinsically Non-linear Model I
• 10 Analysis of Covariance (ANCOVA)
• 11 Multiple Decision Problems
• 12 Experimental Designs
• Appendix A: Symbolism
• Appendix B: Abbreviations
• Appendix C: Probability and Density Functions
• Appendix D: Tables
• Solutions and Hints for Exercises
• Index Mathematical Statistics
• End User License Agreement