Preface
Acknowledgments
Part I THEORY
Introduction
1.1 Distribution of extremes in random fields
1.2 Outline of the method
1.3 Gaussian and asymptotically Gaussian random fields
1.4 Applications
Basic examples
2.1 Introduction
2.2 A power-one sequential test
2.3 A kernel-based scanning statistic
2.4 Other methods
3 Approximation of the local rate
3.1 Introduction
3.2 Preliminary localization and approximation
3.2.1 Localization
3.2.2 A discrete approximation
3.3 Measure transformation
3.4 Application of the localization theorem
3.4.1 Checking Condition Ⅰ
3.4.2 Checking Condition Ⅴ
3.4.3 Checking Condition Ⅳ
3.4.4 Checking Condition Ⅱ
3.4.5 Checking Condition Ⅲ
3.5 Integration
4 From the local to the global
4.1 Introduction
4.2 Poisson approximation.of probabilities
4.3 Average run length to false alarm
The localization theorem
5.1 Introduction
5.2 A simplified version of the localization theorem
5.3 The localization theorem
5.4 A local limit theorem
5.5 Edge effects and higher order approximations
Part Ⅱ APPLICATIONS
Nonparametric tests: Kolmogorov-Smirnov and Peacock
6.1 Introduction
6.1.1 Classical analysis of the Kolmogorov-Smimov test
6.1.2 Peacock''s test
6.2 Analysis of the one-dimensional case
6.2.1 Preliminary localization
6.2.2 An approximation by a discrete grid
6.2.3 Measure transformation
6.2.4 The asymptotic distribution of the local field and the
global term
6.2.5 Application of the localization theorem and integration
6.2.6 Checking the conditions of the localization theorem
6.3 Peacock''s test
6.4 Relations to scanning statistics
……
References
Index
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