前辅文
Part I THEORY
1 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
2 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
3.3 Measure transformation
3.4 Application of the localization theorem
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
5 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
6 Nonparametric tests: Kolmogorov-Smirnov and Peacock
6.1 Introduction
6.2 Analysis of the one-dimensional case
6.3 Peacock's test
6.4 Relations to scanning statistics
7 Copy number variations
7.1 Introduction
7.2 The statistical model
7.3 Analysis of statistical properties
7.4 The false discovery rate
8 Sequential monitoring of an image
8.1 Introduction
8.2 The statistical model
8.3 Analysis of statistical properties
8.4 Optimal change-point detection
9 Buffer overflow
9.1 Introduction
9.2 The statistical model
9.3 Analysis of statistical properties
9.4 Heavy tail distribution, long-range dependence, and self-similarity
10 Computing Pickands' constants
10.1 Introduction
10.2 Representations of constants
10.3 Analysis of statistical error
10.4 Enumerating the effect of local fluctuations
Appendix: Mathematical background
A.1 Transforms
A.2 Approximations of sum of independent random elements
A.3 Concentration inequalities
A.4 Random walks
A.5 Renewal theory
A.6 The Gaussian distribution
A.7 Large sample inference
A.8 Integration
A.9 Poisson approximation
A.10 Convexity
References
Index
