03812nam 2200577 a 450 991082170590332120200520144314.01-118-72060-11-118-72061-X(CKB)2550000001111868(EBL)1434101(OCoLC)862047261(SSID)ssj0000981849(PQKBManifestationID)11546229(PQKBTitleCode)TC0000981849(PQKBWorkID)10982682(PQKB)11209710(MiAaPQ)EBC1434101(Au-PeEL)EBL1434101(CaPaEBR)ebr10748708(PPN)191455806(EXLCZ)99255000000111186820130619d2013 uy 0engur|n|---|||||txtccrExtremes in random fields[electronic resource] a theory and its applications /Benjamin YakirChichester, West Sussex, U.K. John Wiley & Sons Inc.20131 online resource (254 p.)Wiley series in probability and statisticsDescription based upon print version of record.1-118-62020-8 1-299-80509-4 Includes bibliographical references and index.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."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"--Provided by publisher.Wiley Series in Probability and StatisticsRandom fieldsRandom fields.519.2/3MAT029000bisacshYakir Benjamin1607942MiAaPQMiAaPQMiAaPQBOOK9910821705903321Extremes in random fields3934416UNINA