随机域中的极值统计学 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

随机域中的极值统计学 英文版PDF格式电子书版下载

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Part Ⅰ THEORY1

1 Introduction3

1.1 Distribution of extremes in random fields3

1.2 Outline of the method7

1.3 Gaussian and asymptotically Gaussian random fields9

1.4 Applications11

2 Basic examples15

2.1 Introduction15

2.2 A power-one sequential test15

2.3 A kernel-based scanning statistic24

2.4 Other methods38

3 Approximation of the local rate41

3.1 Introduction41

3.2 Preliminary localization and approximation43

3.2.1 Localization43

3.2.2 A discrete approximation46

3.3 Measure transformation51

3.4 Application of the localization theorem55

3.4.1 Checking Condition Ⅰ57

3.4.2 Checking Condition Ⅴ57

3.4.3 Checking Condition Ⅳ58

3.4.4 Checking Condition Ⅱ59

3.4.5 Checking Condition Ⅲ63

3.5 Integration67

4 From the local to the global71

4.1 Introduction71

4.2 Poisson approximation of probabilities72

4.3 Average run length to false alarm78

5 The localization theorem87

5.1 Introduction87

5.2 A simplified version of the localization theorem88

5.3 The localization theorem90

5.4 A local limit theorem95

5.5 Edge effects and higher order approximations100

Part Ⅱ APPLICATIONS103

6 Nonparametric tests:Kolmogorov-Smirnov and Peacock105

6.1 Introduction105

6.1.1 Classical analysis of the Kolmogorov-Smirnov test106

6.1.2 Peacock's test108

6.2 Analysis of the one-dimensional case109

6.2.1 Preliminary localization110

6.2.2 An approximation by a discrete grid111

6.2.3 Measure transformation114

6.2.4 The asymptotic distribution of the local field and the global term115

6.2.5 Application of the localization theorem and integration117

6.2.6 Checking the conditions of the localization theorem119

6.3 Peacock's test120

6.4 Relations to scanning statistics123

7 Copy number variations125

7.1 Introduction125

7.2 The statistical model127

7.3 Analysis of statistical properties131

7.3.1 The alternative distribution131

7.3.2 Preliminary localization and approximation132

7.3.3 Measure transformation132

7.3.4 The localization theorem and the local limit theorem133

7.3.5 Checking Condition Ⅴ＊137

7.3.6 Checking Condition Ⅱ＊137

7.4 The false discovery rate140

8 Sequential monitoring of an image143

8.1 Introduction143

8.2 The statistical model146

8.3 Analysis of statistical properties148

8.3.1 Preliminary localization149

8.3.2 Measure transformation,the localization theorem,and integration155

8.3.3 Checking the conditions of the localization theorem157

8.3.4 Checking Condition Ⅴ157

8.3.5 Checking Condition Ⅳ158

8.3.6 Checking Condition Ⅱ159

8.4 Optimal change-point detection161

9 Buffer overflow165

9.1 Introduction165

9.2 The statistical model169

9.2.1 The process of demand from a single source169

9.2.2 The integrated process of demand171

9.3 Analysis of statistical properties172

9.3.1 The large deviation factor172

9.3.2 Preliminary localization174

9.3.3 Approximation by a cruder grid175

9.3.4 Measure transformation179

9.3.5 The localization theorem180

9.3.6 Integration183

9.3.7 Checking the conditions of the localization theorem184

9.3.8 Checking Condition Ⅳ184

9.3.9 Checking Condition Ⅴ185

9.3.10 Checking Condition Ⅱ185

9.4 Heavy tail distribution,long-range dependence,and self-similarity186

10 Computing Pickands'constants191

10.1 Introduction191

10.1.1 The double-sum method192

10.1.2 The method based on the likelihood ratio identity193

10.1.3 Pickands'constants195

10.2 Representations of constants196

10.3 Analysis of statistical error199

10.4 Enumerating the effect of local fluctuations204

Appendix:Mathematical background209

A.1 Transforms209

A.2 Approximations of sum of independent random elements211

A.3 Concentration inequalities214

A.4 Random walks215

A.5 Renewal theory215

A.6 The Gaussian distribution216

A.7 Large sample inference217

A.8 Integration218

A.9 Poisson approximation219

A.10 Convexity220

References221

Index223