Extremes in random fields : a theory and its applications /
"Reading chapters of the book can be used as a primer for a student who is then required to analyze a new problem that was not digested for him/her in the book"--
Κύριος συγγραφέας: | |
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Μορφή: | Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Chichester, West Sussex, United Kingdom :
John Wiley & Sons Inc.,
2013.
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Σειρά: | Wiley series in probability and statistics.
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Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Περίληψη: | "Reading chapters of the book can be used as a primer for a student who is then required to analyze a new problem that was not digested for him/her in the book"-- |
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Περιγραφή τεκμηρίου: | Machine generated contents note: Preface 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 3.2.1 Localization 3.2.2 A discrete 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 simplifies version of the localization theorem 5.3 The Localization Theorem 5.4 A local limit theorem 5.5 Edge effects II Applications 6 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 (FDR) 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 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 Local fluctuations Appendix A 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. |
Φυσική περιγραφή: | 1 online resource. |
Βιβλιογραφία: | Includes bibliographical references and index. |
ISBN: | 9781118720622 1118720628 9781118720615 111872061X 9781118720639 1118720636 9781118720608 1118720601 1118620208 9781118620205 |
DOI: | 10.1002/9781118720608 |