Mathematical Statistics
- 7h 54m
- Dieter Rasch, Dieter Schott
- John Wiley & Sons (UK)
- 2018
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.
About the Authors
DIETER RASCH, PhD, is scientific advisor at the Center for Design of Experiments at the University of Natural Resources and Life Sciences, Vienna, Austria. He has published more than 275 scientific papers and 56 books as author or editor.
DIETER SCHOTT obtained his PhD in analysis from the University of Rostock in 1976 and did his habilitation in the field of numerical functional analysis in 1982. He has published more than 100 scientific papers and is active as author, co-author and editor of numerous books and scientific journals.
In this Book
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Basic Ideas of Mathematical Statistics
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Point Estimation
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Statistical Tests and Confidence Estimations
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Linear Models – General Theory
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Analysis of Variance (ANOVA) – Fixed Effects Models (Model I of Analysis of Variance)
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Analysis of Variance—Estimation of Variance Components (Model II of the Analysis of Variance)
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Analysis of Variance – Models with Finite Level Populations and Mixed Models
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Regression Analysis – Linear Models with Non-random Regressors (Model I of Regression Analysis) and with Random Regressors (Model II of Regression Analysis)
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Regression Analysis – Intrinsically Non-linear Model I
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Analysis of Covariance (ANCOVA)
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Multiple Decision Problems
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Experimental Designs
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