Statistical Hypothesis Testing : Theory and Methods
by Shi, Ning-zhong; Tao, JianFormat: Hardcover
Pub. Date: 2008-09-29
Publisher(s): World Scientific Pub Co Inc
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Summary
"This book presents up-to-date theory and methods of statistical hypothesis testing based on measure theory. The so-called statistical space is a measurable space adding a family of probability measures. Most topics in the book will be developed based on this term. The book includes some typical data sets, such as the relation between race and the death penalty verdict, the behavior of food intake of two kinds of Zucker rats, and the per capita income and expenditure in China during the 1978-2002 period. Emphasis is given to the process of finding appropriate statistical techniques and methods of evaluating these techniques."--BOOK JACKET.
Table of Contents
| Preface | p. vii |
| Statistical Spaces | p. 1 |
| Basic Properties of Statistical Spaces | p. 2 |
| Measure in Statistical Spaces | p. 2 |
| Equivalence and Divisibility of Family of Probability Distributions | p. 8 |
| Conditional Probability and Sufficient Statistics | p. 12 |
| Statistics and Random Variables | p. 13 |
| Conditional Probability | p. 15 |
| Sufficient Statistics | p. 20 |
| Exponential Family and Completeness | p. 27 |
| Exponential Family | p. 28 |
| Completeness | p. 30 |
| Sufficiency and Completeness | p. 34 |
| Ancillary Statistics | p. 35 |
| Estimation Methods Based on Statistical Space | p. 37 |
| Moment Estimation and Median Estimation | p. 37 |
| Maximum Likelihood Estimators | p. 40 |
| Quality of Estimators | p. 46 |
| Comparison of Estimators | p. 51 |
| Nonparametric MLE for Population cdf | p. 55 |
| Problems | p. 58 |
| Methods of Statistical Tests | p. 65 |
| Introduction: Background of Problem | p. 65 |
| Likelihood Ratio Tests | p. 72 |
| The Likelihood Ratio Methods | p. 72 |
| LRT's Limiting Distribution | p. 79 |
| Tests of Goodness-of-fit | p. 86 |
| Limiting Distribution | p. 87 |
| Test of Independence in Two-Way Contingency Table | p. 90 |
| Test of Independence in Three-Way Contingency Table | p. 92 |
| Goodness-of-Fit Test of Distribution Function | p. 95 |
| Sign Tests and Rank Tests | p. 96 |
| Sign Tests | p. 97 |
| Wilcoxon Signed Rank Tests | p. 98 |
| Wilcoxon Rank Tests | p. 102 |
| U-I Tests | p. 104 |
| Empirical Likelihood-Ratio Tests | p. 108 |
| Problems | p. 112 |
| The Comparison of Test Statistics | p. 117 |
| Probability of Two Types of Error in Hypothesis Test | p. 117 |
| Neyman-Pearson Fundamental Lemma | p. 121 |
| Unbiased Test | p. 133 |
| Comparing Power Functions | p. 141 |
| Test Procedures | p. 141 |
| Power Functions and Their Comparison | p. 145 |
| Comparing Robustness | p. 148 |
| Efficiency of Tests | p. 148 |
| Asymptotic Relative Efficiency | p. 151 |
| Interval Estimation Based on Test | p. 154 |
| Interval Estimation and Acceptance Region | p. 156 |
| Uniformly Most Accurate Confidence Interval | p. 158 |
| Uniformly Most Accurate Unbiased Confidence Interval | p. 160 |
| Uniformly Most Accuracy and Interval Length | p. 165 |
| Problems | p. 166 |
| Parametric Tests for Simple Models | p. 175 |
| One-Factor Model: Analysis of Variance | p. 175 |
| One-Factor Model: Multiple Comparisons | p. 181 |
| Multiple Comparisons | p. 182 |
| Generalized Multiple Comparisons | p. 186 |
| The False Discovery Rate Procedure | p. 189 |
| One-Factor Model: Trend Tests | p. 191 |
| Linearity Tests | p. 192 |
| Likelihood Ratio Test | p. 197 |
| Linear Rank Tests | p. 210 |
| Multi-Factor Model: Analysis of Variance | p. 213 |
| Model Without Interaction Effects | p. 213 |
| Model with Interaction Effects | p. 217 |
| Multi-Factor Model: Log-linear Models | p. 219 |
| Two-Dimensional Contingency Table | p. 219 |
| Three-Dimensional Contingency Table | p. 223 |
| Ancillary Parameter Model | p. 226 |
| Problems | p. 227 |
| Parametric Tests for Regression Models | p. 235 |
| Linear Models | p. 235 |
| Establishment of Model | p. 235 |
| Estimating and Testing the Parameters | p. 240 |
| Centralization | p. 245 |
| Regression Models | p. 248 |
| Regression Model and Linear Model | p. 248 |
| Errors-in-Variables Model | p. 251 |
| Logistic Regression Models | p. 256 |
| One-Variable Case | p. 257 |
| Multivariable Case | p. 263 |
| Time Series: Trend Term Models | p. 264 |
| Time Series: Autoregressive Models | p. 271 |
| Random Walk and Brownian Motion | p. 271 |
| Autoregressive Model | p. 273 |
| Granger Causality Tests | p. 281 |
| Granger Causality | p. 281 |
| Integration of Order d | p. 284 |
| Real Data Analysis | p. 286 |
| Problems | p. 288 |
| Bibliography | p. 297 |
| Index | p. 303 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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