LEADER 04402nam 22006375 450 001 9910897973803321 005 20260119155621.0 010 $a9783662689233 010 $a3662689235 024 7 $a10.1007/978-3-662-68923-3 035 $a(CKB)36382628800041 035 $a(DE-He213)978-3-662-68923-3 035 $a(MiAaPQ)EBC31733029 035 $a(Au-PeEL)EBL31733029 035 $a(EXLCZ)9936382628800041 100 $a20241019d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Stochastics $eAn Introduction with a View towards Statistics /$fby Norbert Henze 205 $a1st ed. 2024. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2024. 215 $a1 online resource (XIX, 467 p.) 225 1 $aMathematics Study Resources,$x2731-3832 ;$v10 311 08$a9783662689226 311 08$a3662689227 320 $aIncludes bibliographical references and index. 327 $aPreface -- List of Symbols -- 1 Prerequisites from Probability Theory -- 2 A Poisson Limit Theorem for Triangular Arrays -- 3 The Method of Moments -- 4 A Central Limit Theorem for Stationary m-Dependent Sequences -- 5 The multivariate normal distribution -- 6 Convergence in Distribution and Central Limit Theorem in Rd -- 7 Empirical Distribution Function -- 8 Limit Theorems for U-Statistics -- 9 Basic Concepts of Estimation Theory -- 10 Maximum Likelihood Estimation -- 11 Asymptotic (relative) efficiency of estimators -- 12 Likelihood Ratio Tests -- 13 Probability Measures on Metric Spaces -- 14 Convergence of Distributions in Metric Spaces -- 15 Wiener Process, Donsker?s Theorem, and Brownian Bridge -- 16 The Space D[0,1], Empirical Processes -- 17 Random Elements in Separable Hilbert Spaces -- Afterword -- Solutions to the Problems -- Bibliography -- Index. 330 $aThis textbook, which is based on the second edition of a book that has been previously published in German language, provides a comprehension-oriented introduction to asymptotic stochastics. It is aimed at the beginning of a master's degree course in mathematics and covers the material that can be taught in a four-hour lecture with two-hour exercises. Individual chapters are also suitable for seminars at the end of a bachelor's degree course. In addition to more basic topics such as the method of moments in connection with the convergence in distribution or the multivariate central limit theorem and the delta method, the book covers limit theorems for U-statistics, the Wiener process and Donsker's theorem, as well as the Brownian bridge, with applications to statistics. It concludes with a central limit theorem for triangular arrays of Hilbert space-valued random elements with applications to weighted L² statistics. The book is deliberately designed for self-study. It contains 138 self-questions, which are answered at the end of each chapter, as well as 194 exercises with solutions. The Author Norbert Henze is a retired professor of stochastics at the Karlsruhe Institute of Technology (KIT). He was awarded the Ars legendi Faculty Prize 2014 for excellent university teaching in mathematics. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. 410 0$aMathematics Study Resources,$x2731-3832 ;$v10 606 $aProbabilities 606 $aStatistics 606 $aProbability Theory 606 $aStatistics 606 $aEstadística$2thub 606 $aProbabilitats$2thub 606 $aProcessos estocàstics$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 0$aStatistics. 615 14$aProbability Theory. 615 24$aStatistics. 615 7$aEstadística 615 7$aProbabilitats 615 7$aProcessos estocàstics 676 $a519.2 700 $aHenze$b Norbert$f1951-$01229276 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897973803321 996 $aAsymptotic Stochastics$94212194 997 $aUNINA