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E-raamat: Statistical Hypothesis Testing: Theory And Methods

(Northeast Normal Univ, China), (Northeast Normal Univ, China)
  • Formaat: 320 pages
  • Ilmumisaeg: 29-Sep-2008
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813107212
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Statistical Hypothesis Testing: Theory And MethodsSuurem pilt
  • Formaat: 320 pages
  • Ilmumisaeg: 29-Sep-2008
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789813107212
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This work presents theory and methods of statistical hypothesis testing based on measure theory, with emphasis on finding and evaluating appropriate statistical techniques. After an introduction to basic properties of statistical space, the next two chapters focus on methods of constructing parametric and non-parametric methods, and on techniques for evaluating statistical methods. Later chapters cover parametric tests for simple models and for regression models, covering topics such as ANOVA, AIC, the log linear model, and the tendency test, which is used in bioinformatics research. Concepts are illustrated with real-life data sets on the relationship between race and the death penalty verdict, food intake of two kinds of rats, and per capita income and expenditure in China. The book's readership includes advanced undergraduate and graduate students majoring in statistics. Shi and Tao are affiliated with Northeast Normal University, China. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)

Preface vii
1. Statistical Spaces 1
1.1 Basic Properties of Statistical Spaces
2
1.1.1 Measure in Statistical Spaces
2
1.1.2 Equivalence and Divisibility of Family of Probability Distributions
8
1.2 Conditional Probability and Sufficient Statistics
12
1.2.1 Statistics and Random Variables
13
1.2.2 Conditional Probability
15
1.2.3 Sufficient Statistics
20
1.3 Exponential Family and Completeness
27
1.3.1 Exponential Family
28
1.3.2 Completeness
30
1.3.3 Sufficiency and Completeness
34
1.3.4 Ancillary Statistics
35
1.4 Estimation Methods Based on Statistical Space
37
1.4.1 Moment Estimation and Median Estimation
37
1.4.2 Maximum Likelihood Estimators
40
1.4.3 Quality of Estimators
46
1.4.4 Comparison of Estimators
51
1.4.5 Nonparametric MLE for Population cdf
55
1.5 Problems
58
2. Methods of Statistical Tests 65
2.1 Introduction: Background of Problem
65
2.2 Likelihood Ratio Tests
72
2.2.1 The Likelihood Ratio Methods
72
2.2.2 LRT's Limiting Distribution
79
2.3 Tests of Goodness-of-fit
86
2.3.1 Limiting Distribution
87
2.3.2 Test of Independence in Two-Way Contingency Table
90
2.3.3 Test of Independence in Three-Way Contingency Table
92
2.3.4 Goodness-of-Fit Test of Distribution Function
95
2.4 Sign Tests and Rank Tests
96
2.4.1 Sign Tests
97
2.4.2 Wilcoxon Signed Rank Tests
98
2.4.3 Wilcoxon Rank Tests
102
2.5 U-I Tests
104
2.6 Empirical Likelihood-Ratio Tests
108
2.7 Problems
112
3. The Comparison of Test Statistics 117
3.1 Probability of Two Types of Error in Hypothesis Test
117
3.2 Neyman-Pearson Fundamental Lemma
121
3.3 Unbiased Test
133
3.4 Comparing Power Functions
141
3.4.1 Test Procedures
141
3.4.2 Power Functions and Their Comparison
145
3.5 Comparing Robustness
148
3.5.1 Efficiency of Tests
148
3.5.2 Asymptotic Relative Efficiency
151
3.6 Interval Estimation Based on Test
154
3.6.1 Interval Estimation and Acceptance Region
156
3.6.2 Uniformly Most Accurate Confidence Interval
158
3.6.3 Uniformly Most Accurate Unbiased Confidence Interval
160
3.6.4 Uniformly Most Accuracy and Interval Length
165
3.7 Problems
166
4. Parametric Tests for Simple Models 175
4.1 One-Factor Model: Analysis of Variance
175
4.2 One-Factor Model: Multiple Comparisons
181
4.2.1 Multiple Comparisons
182
4.2.2 Generalized Multiple Comparisons
186
4.2.3 The False Discovery Rate Procedure
189
4.3 One-Factor Model: Trend Tests
191
4.3.1 Linearity Tests
192
4.3.2 Likelihood Ratio Test
197
4.3.3 Linear Rank Tests
210
4.4 Multi-Factor Model: Analysis of Variance
213
4.4.1 Model Without Interaction Effects
213
4.4.2 Model with Interaction Effects
217
4.5 Multi-Factor Model: Log-linear Models
219
4.5.1 Two-Dimensional Contingency Table
219
4.5.2 Three-Dimensional Contingency Table
223
4.5.3 Ancillary Parameter Model
226
4.6 Problems
227
5. Parametric Tests for Regression Models 235
5.1 Linear Models
235
5.1.1 Establishment of Model
235
5.1.2 Estimating and Testing the Parameters
240
5.1.3 Centralization
245
5.2 Regression Models
248
5.2.1 Regression Model and Linear Model
248
5.2.2 Errors-in-Variables Model
251
5.3 Logistic Regression Models
256
5.3.1 One-Variable Case
257
5.3.2 Multivariable Case
263
5.4 Time Series: Trend Term Models
264
5.5 Time Series: Autoregressive Models
271
5.5.1 Random Walk and Brownian Motion
271
5.5.2 Autoregressive Model
273
5.6 Granger Causality Tests
281
5.6.1 Granger Causality
281
5.6.2 Integration of Order d
284
5.6.3 Real Data Analysis
286
5.7 Problems
288
Bibliography 297
Index 303
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