Buch, Englisch, 688 Seiten, Format (B × H): 156 mm x 236 mm, Gewicht: 961 g
Buch, Englisch, 688 Seiten, Format (B × H): 156 mm x 236 mm, Gewicht: 961 g
ISBN: 978-1-119-38528-8
Verlag: Wiley
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.
Autoren/Hrsg.
Weitere Infos & Material
Preface xiii
1 Basic Ideas of Mathematical Statistics 1
1.1 Statistical Population and Samples 2
1.1.1 Concrete Samples and Statistical Populations 2
1.1.2 Sampling Procedures 4
1.2 Mathematical Models for Population and Sample 8
1.3 Sufficiency and Completeness 9
1.4 The Notion of Information in Statistics 20
1.5 Statistical Decision Theory 28
1.6 Exercises 32
References 37
2 Point Estimation 39
2.1 Optimal Unbiased Estimators 41
2.2 Variance-Invariant Estimation 53
2.3 Methods for Construction and Improvement of Estimators 57
2.3.1 Maximum Likelihood Method 57
2.3.2 Least Squares Method 60
2.3.3 Minimum Chi-Squared Method 61
2.3.4 Method of Moments 62
2.3.5 Jackknife Estimators 63
2.3.6 Estimators Based on Order Statistics 64
2.3.6.1 Order and Rank Statistics 64
2.3.6.2 L-Estimators 66
2.3.6.3 M-Estimators 67
2.3.6.4 R-Estimators 68
2.4 Properties of Estimators 68
2.4.1 Small Samples 69
2.4.2 Asymptotic Properties 71
2.5 Exercises 75
References 78
3 Statistical Tests and Confidence Estimations 79
3.1 Basic Ideas of Test Theory 79
3.2 The Neyman–Pearson Lemma 87
3.3 Tests for Composite Alternative Hypotheses and One-Parametric Distribution Families 96
3.3.1 Distributions with Monotone Likelihood Ratio and Uniformly Most Powerful Tests for One-Sided Hypotheses 96
3.3.2 UMPU-Tests for Two-Sided Alternative Hypotheses 105
3.4 Tests for Multi-Parametric Distribution Families 110
3.4.1 General Theory 111
3.4.2 The Two-Sample Problem: Properties of Various Tests and Robustness 124
3.4.2.1 Comparison of Two Expectations 125
3.4.3 Comparison of Two Variances 137
3.4.4 Table for Sample Sizes 138
3.5 Confidence Estimation 139
3.5.1 One-Sided Confidence Intervals in One-Parametric Distribution Families 140
3.5.2 Two-Sided Confidence Intervals in One-Parametric and Confidence Intervals in Multi-Parametric Distribution Families 143
3.5.3 Table for Sample Sizes 146
3.6 Sequential Tests 147
3.6.1 Introduction 147
3.6.2 Wald’s Sequential Likelihood Ratio Test for One-Parametric Exponential Families 149
3.6.3 Test about Mean Values for Unknown Variances 153
3.6.4 Approximate Tests for the Two-Sample Problem 158
3.6.5 Sequential Triangular Tests 160
3.6.6 A Sequential Triangular Test for the Correlation Coefficient 162
3.7 Remarks about Interpretation 169
3.8 Exercises 170
References 176
4 Linear Models: General Theory 179
4.1 Linear Models with Fixed Effects 179
4.1.1 Least Squares Method 180
4.1.2 Maximum Likelihood Method 184
4.1.3 Tests of Hypotheses 185
4.1.4 Construction of Confidence Regions 190
4.1.5 Special Linear Models 191
4.1.6 The Generalised Least Squares Method (GLSM) 198
4.2 Linear Models with Random Effects: Mixed Models 199
4.2.1 Best Linear Unbiased Prediction (BLUP) 200
4.2.2 Estimation of Variance Components 202
4.3 Exercises 203
References 204
5 Analysis of Variance (ANOVA): Fixed Effects Models (Model I of Analysis of Variance) 207
5.1 Introduction 207
5.2 Analysis of Variance with One Factor (Simple- or One-Way Analysis of Variance) 215
5.2.1 The Model and the Analysis 215
5.2.2 Planning the Size of an Experiment 228
5.2.2.1 General Description for All Sections of This Chapter 228
5.2.2.2 The Experimental Size for the One-Way Classification 231
5.3 Two-Way Analysis of Variance 232
5.3.1 Cross-Classification (A × B) 233
5.3.1.1 Parameter Estimation 236
5.3.1.2 Testing Hypotheses 244
5.3.2 Nested Classification (A B) 260
5.4 Three-Way Classification 272
5.4.1 Complete Cross-Classification (A × B × C) 272
5.4
