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Theoretical Statistics
Topics for a Core Course
Taschenbuch von Robert W. Keener
Sprache: Englisch

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Beschreibung
Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential.

The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis.

The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.
Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential.

The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis.

The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix.
Über den Autor
Robert Keener is Professor of Statistics at the University of Michigan and a fellow of the Institute of Mathematical Statistics.
Zusammenfassung
Comprehensive coverage of estimation and hypothesis testing, frequentist and Bayesian paradigms, large and small sample methods, and the theory underlying numerical algorithms

Detailed and rigorous exposition designed to make the material clear and accessible

Rich collection of exercises, many with solutions, pushing students to learn the material well enough to use it in their own research and helping them appreciate its relevance to diverse applications
Inhaltsverzeichnis
Probability and Measure.- Exponential Families.- Risk, Sufficiency, Completeness, and Ancillarity.- Unbiased Estimation.- Curved Exponential Families.- Conditional Distributions.- Bayesian Estimation.- Large-Sample Theory.- Estimating Equations and Maximum Likelihood.- Equivariant Estimation.- Empirical Bayes and Shrinkage Estimators.- Hypothesis Testing.- Optimal Tests in Higher Dimensions.- General Linear Model.- Bayesian Inference: Modeling and Computation.- Asymptotic Optimality1.- Large-Sample Theory for Likelihood Ratio Tests.- Nonparametric Regression.- Bootstrap Methods.- Sequential Methods.
Details
Erscheinungsjahr: 2012
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 556
Reihe: Springer Texts in Statistics
Inhalt: xviii
538 S.
ISBN-13: 9781461426707
ISBN-10: 1461426707
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Keener, Robert W.
Auflage: 2010
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Texts in Statistics
Maße: 235 x 155 x 30 mm
Von/Mit: Robert W. Keener
Erscheinungsdatum: 05.11.2012
Gewicht: 0,832 kg
preigu-id: 106171229
Über den Autor
Robert Keener is Professor of Statistics at the University of Michigan and a fellow of the Institute of Mathematical Statistics.
Zusammenfassung
Comprehensive coverage of estimation and hypothesis testing, frequentist and Bayesian paradigms, large and small sample methods, and the theory underlying numerical algorithms

Detailed and rigorous exposition designed to make the material clear and accessible

Rich collection of exercises, many with solutions, pushing students to learn the material well enough to use it in their own research and helping them appreciate its relevance to diverse applications
Inhaltsverzeichnis
Probability and Measure.- Exponential Families.- Risk, Sufficiency, Completeness, and Ancillarity.- Unbiased Estimation.- Curved Exponential Families.- Conditional Distributions.- Bayesian Estimation.- Large-Sample Theory.- Estimating Equations and Maximum Likelihood.- Equivariant Estimation.- Empirical Bayes and Shrinkage Estimators.- Hypothesis Testing.- Optimal Tests in Higher Dimensions.- General Linear Model.- Bayesian Inference: Modeling and Computation.- Asymptotic Optimality1.- Large-Sample Theory for Likelihood Ratio Tests.- Nonparametric Regression.- Bootstrap Methods.- Sequential Methods.
Details
Erscheinungsjahr: 2012
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 556
Reihe: Springer Texts in Statistics
Inhalt: xviii
538 S.
ISBN-13: 9781461426707
ISBN-10: 1461426707
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Keener, Robert W.
Auflage: 2010
Hersteller: Springer New York
Springer US, New York, N.Y.
Springer Texts in Statistics
Maße: 235 x 155 x 30 mm
Von/Mit: Robert W. Keener
Erscheinungsdatum: 05.11.2012
Gewicht: 0,832 kg
preigu-id: 106171229
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