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Asymptotic Statistics
Buch von Rabi Bhattacharya (u. a.)
Sprache: Englisch

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Beschreibung
These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 §1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx) < 00, for some integer s;::: 3, and that Q is normalized, (1.2) J x(i)Q(dx) = 0 (1 ~ i ~ k), J x(i)x(j)Q(dx) = Dij (1 ~ i,j ~ k).
These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 §1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx) < 00, for some integer s;::: 3, and that Q is normalized, (1.2) J x(i)Q(dx) = 0 (1 ~ i ~ k), J x(i)x(j)Q(dx) = Dij (1 ~ i,j ~ k).
Inhaltsverzeichnis
I: Asymptotic Expansions in Statistics1 by Rabi Bhattacharya.- §1. Cramér-Egeworth Expansions.- §2. Expansions of Distributions of Statistics Admitting Stochastic Expansions.- §3. Cornish-Fisher Expansions.- §4. Second Order Efficiency.- §5. Bootstrap and Edgeworth Expansion.- §6. Notes and References.- References.- II: Weak Convergence in Nonparametric Statistics by Manfred Denker.- 1: Symmetric Statistics.- 2: Statistics Based on Ranking Methods.
Details
Erscheinungsjahr: 1990
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: 122 S.
ISBN-13: 9783764322823
ISBN-10: 3764322829
Sprache: Englisch
Einband: Gebunden
Autor: Bhattacharya, Rabi
Denker, Manfred
Hersteller: Birkhäuser Basel
Springer Basel AG
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 12 mm
Von/Mit: Rabi Bhattacharya (u. a.)
Erscheinungsdatum: 01.04.1990
Gewicht: 0,36 kg
Artikel-ID: 102120966
Inhaltsverzeichnis
I: Asymptotic Expansions in Statistics1 by Rabi Bhattacharya.- §1. Cramér-Egeworth Expansions.- §2. Expansions of Distributions of Statistics Admitting Stochastic Expansions.- §3. Cornish-Fisher Expansions.- §4. Second Order Efficiency.- §5. Bootstrap and Edgeworth Expansion.- §6. Notes and References.- References.- II: Weak Convergence in Nonparametric Statistics by Manfred Denker.- 1: Symmetric Statistics.- 2: Statistics Based on Ranking Methods.
Details
Erscheinungsjahr: 1990
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: 122 S.
ISBN-13: 9783764322823
ISBN-10: 3764322829
Sprache: Englisch
Einband: Gebunden
Autor: Bhattacharya, Rabi
Denker, Manfred
Hersteller: Birkhäuser Basel
Springer Basel AG
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 12 mm
Von/Mit: Rabi Bhattacharya (u. a.)
Erscheinungsdatum: 01.04.1990
Gewicht: 0,36 kg
Artikel-ID: 102120966
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