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020 _a9783662689233
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024 7 _a10.1007/978-3-662-68923-3
_2doi
050 4 _aQA273.A1-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
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072 7 _aPBWL
_2thema
100 1 _aHenze, Norbert.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986296
245 1 0 _aAsymptotic Stochastics
_h[electronic resource] :
_bAn Introduction with a View towards Statistics /
_cby Norbert Henze.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aXIX, 467 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics Study Resources,
_x2731-3832 ;
_v10
505 0 _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.
520 _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.
650 0 _aProbabilities.
_965724
650 0 _aStatistics .
_965982
650 1 4 _aProbability Theory.
_967428
650 2 4 _aStatistics.
_965982
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662689226
776 0 8 _iPrinted edition:
_z9783662689240
830 0 _aMathematics Study Resources,
_x2731-3832 ;
_v10
_981153
856 4 0 _uhttps://doi.org/10.1007/978-3-662-68923-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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