Bickel / Doksum Mathematical Statistics

Basic Ideas and Selected Topics, Volume I, Second Edition
2. Auflage 2015
ISBN: 978-1-4987-2381-7
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 576 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods.

The book first discusses non- and semiparametric models before covering parameters and parametric models. It then offers a detailed treatment of maximum likelihood estimates (MLEs) and examines the theory of testing and confidence regions, including optimality theory for estimation and elementary robustness considerations. It next presents basic asymptotic approximations with one-dimensional parameter models as examples. The book also describes inference in multivariate (multiparameter) models, exploring asymptotic normality and optimality of MLEs, Wald and Rao statistics, generalized linear models, and more.

Mathematical Statistics: Basic Ideas and Selected Topics, Volume II will be published in 2015. It will present important statistical concepts, methods, and tools not covered in Volume I.

Autoren/Hrsg.

Bickel, Peter J.

Doksum, Kjell A.

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftsstatistik, Demographie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

STATISTICAL MODELS, GOALS, AND PERFORMANCE CRITERIA

Data, Models, Parameters, and Statistics
Bayesian Models

The Decision Theoretic Framework
Prediction

Sufficiency

Exponential Families

METHODS OF ESTIMATION

Basic Heuristics of Estimation

Minimum Contrast Estimates and Estimating Equations

Maximum Likelihood in Multiparameter Exponential Families
Algorithmic Issues

MEASURES OF PERFORMANCE

Introduction

Bayes Procedures

Minimax Procedures

Unbiased Estimation and Risk Inequalities

Nondecision Theoretic Criteria

TESTING AND CONFIDENCE REGIONS

Introduction

Choosing a Test Statistic: The Neyman-Pearson Lemma

Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models

Confidence Bounds, Intervals, and Regions
The Duality between Confidence Regions and Tests

Uniformly Most Accurate Confidence Bounds

Frequentist and Bayesian Formulations

Prediction Intervals

Likelihood Ratio Procedures

ASYMPTOTIC APPROXIMATIONS

Introduction: The Meaning and Uses of Asymptotics

Consistency

First- and Higher-Order Asymptotics: The Delta Method with Applications

Asymptotic Theory in One Dimension

Asymptotic Behavior and Optimality of the Posterior Distribution

INFERENCE IN THE MULTIPARAMETER CASE

Inference for Gaussian Linear Models

Asymptotic Estimation Theory in p Dimensions

Large Sample Tests and Confidence Regions

Large Sample Methods for Discrete Data

Generalized Linear Models

Robustness Properties and Semiparametric Models

APPENDIX A: A REVIEW OF BASIC PROBABILITY THEORY
APPENDIX B: ADDITIONAL TOPICS IN PROBABILITY AND ANALYSIS
APPENDIX C: TABLES

INDEX

Problems and Complements, Notes, and References appear at the end of each chapter.

Über Autor(innen)

Peter J. Bickel is a professor emeritus in the Department of Statistics and a professor in the Graduate School at the University of California, Berkeley. Dr. Bickel is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. He has been a Guggenheim Fellow and MacArthur Fellow, a recipient of the COPSS Presidents’ Award, and president of the Bernoulli Society and the Institute of Mathematical Statistics. He holds honorary doctorate degrees from the Hebrew University of Jerusalem and ETH Zurich.

Kjell A. Doksum is a senior scientist in the Department of Statistics at the University of Wisconsin–Madison. His research encompasses the estimation of nonparametric regression and correlation curves, inference for global measures of association in semiparametric and nonparametric settings, the estimation of regression quantiles, statistical modeling and analysis of HIV data, the analysis of financial data, and Bayesian nonparametric inference.