Extremes in Random Fields : a Theory and Its Applications.

Presents a useful new technique for analyzing the extreme-value behaviour of random fields Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on th...

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Bibliographic Details
Main Author: Yakir, Benjamin
Format: eBook
Published: Hoboken : Wiley, 2013.
Series:Wiley series in probability and statistics
Online Access:Click for online access
Table of Contents:
  • Cover; Title Page; Copyright; Contents; Preface; Acknowledgments; Part I Theory; Chapter 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; Chapter 2 Basic examples; 2.1 Introduction; 2.2 A power-one sequential test; 2.3 A kernel-based scanning statistic; 2.4 Other methods; Chapter 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 theorem3.4.1 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; Chapter 4 From the local to the global; 4.1 Introduction; 4.2 Poisson approximation of probabilities; 4.3 Average run length to false alarm; Chapter 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.
  • Chapter 6 Nonparametric tests: Kolmogorov-Smirnov and Peacock6.1 Introduction; 6.1.1 Classical analysis of the Kolmogorov-Smirnov 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; Chapter 7 Copy number variations.
  • 7.1 Introduction7.2 The statistical model; 7.3 Analysis of statistical properties; 7.3.1 The alternative distribution; 7.3.2 Preliminary localization and approximation; 7.3.3 Measure transformation; 7.3.4 The localization theorem and the local limit theorem; 7.3.5 Checking Condition V*; 7.3.6 Checking Condition II*; 7.4 The false discovery rate; Chapter 8 Sequential monitoring of an image; 8.1 Introduction; 8.2 The statistical model; 8.3 Analysis of statistical properties; 8.3.1 Preliminary localization; 8.3.2 Measure transformation, the localization theorem, and integration.
  • 8.3.3 Checking the conditions of the localization theorem8.3.4 Checking Condition V*; 8.3.5 Checking Condition IV*; 8.3.6 Checking Condition II*; 8.4 Optimal change-point detection; Chapter 9 Buffer overflow; 9.1 Introduction; 9.2 The statistical model; 9.2.1 The process of demand from a single source; 9.2.2 The integrated process of demand; 9.3 Analysis of statistical properties; 9.3.1 The large deviation factor; 9.3.2 Preliminary localization; 9.3.3 Approximation by a cruder grid; 9.3.4 Measure transformation; 9.3.5 The localization theorem; 9.3.6 Integration.