LEADER 03812nam 2200577 a 450 001 9910821705903321 005 20200520144314.0 010 $a1-118-72060-1 010 $a1-118-72061-X 035 $a(CKB)2550000001111868 035 $a(EBL)1434101 035 $a(OCoLC)862047261 035 $a(SSID)ssj0000981849 035 $a(PQKBManifestationID)11546229 035 $a(PQKBTitleCode)TC0000981849 035 $a(PQKBWorkID)10982682 035 $a(PQKB)11209710 035 $a(MiAaPQ)EBC1434101 035 $a(Au-PeEL)EBL1434101 035 $a(CaPaEBR)ebr10748708 035 $a(PPN)191455806 035 $a(EXLCZ)992550000001111868 100 $a20130619d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExtremes in random fields$b[electronic resource] $ea theory and its applications /$fBenjamin Yakir 210 $aChichester, West Sussex, U.K. $cJohn Wiley & Sons Inc.$d2013 215 $a1 online resource (254 p.) 225 0$aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a1-118-62020-8 311 $a1-299-80509-4 320 $aIncludes bibliographical references and index. 327 $aMachine 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. 330 $a"Reading chapters of the book can be used as a primer for a student who is then required to analyze a new problem that was not digested for him/her in the book"--$cProvided by publisher. 410 0$aWiley Series in Probability and Statistics 606 $aRandom fields 615 0$aRandom fields. 676 $a519.2/3 686 $aMAT029000$2bisacsh 700 $aYakir$b Benjamin$01607942 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821705903321 996 $aExtremes in random fields$93934416 997 $aUNINA