数理统计.基本思想与重点专题.第1卷:第2版:英文
作 者:Peter J. Bickel,Kjell A. Doksum[著] 著
定 价:169
出 版 社:世界图书出版有限公司北京分公司
出版日期:2020年07月01日
页 数:580
装 帧:平装
ISBN:9787519276041
有名统计学家Bickel 和Doksum的两卷集《数理统计:基本思想与专题》,1977年首次出版,目前的这个版本将1977年第1版的扩充为现在的第1卷,第2版,并且又增加了第2卷。在过去的四十年中,数理统计发生了巨大的变化,这部作品把最前沿的数据分析和统计方法,大数据、高维统计融入高等统计的教材,包括了当下统计学的一些热门话题和方法,每一章按照章节配有习题,并且附有解答提示。内容包括:经验过程,不变估计,半参数,蒙特卡洛,非参数,机器学习,变量选择等,有丰富的习题和补充阅读材料,并附有习题全解。
PREFACE TO THE 2015 EDITION
1 STATISTICAL MODELS,GOALS,AND PERFORMANCE CRITERIA
1.1 Data,Models,Parameters,and Statistics
1.1.1 Data and Models
1.1.2 Parametrizations and Parameters
1.1.3 Statistics as Functions on the Sample Space
1.1.4 Examples,Regression Models
1.2 Bayesian Models
1.3 The Decision Theoretic Framework
1.3.1 Components of the Decision Theory Framework
1.3.2 Comparison of Decision Procedures
1.3.3 Bayes and Minimax Criteria
1.4 Prediction
1.5 Sufficiency
1.6 Exponential Families
1.6.1 The One-Parameter Case
1.6.2 The Multiparameter Case
1.6.3 Building Exponential Families
1.6.4 Properties of Exponential Families
1.6.5 Conjugate Families of Prior Distributions
1.7 Problems and Complements
1.8 Notes
1.9 References
2 METHODS OF ESTIMATION
2.1 Basic Heuristics of Estimation
2.1.1 Minimum Contrast Estimates;Estimating Equations
2.1.2 The Plug-In and Extension Principles
2.2 Minimum Contrast Estimates and Estimating Equations
2.2.1 Least Squares and Weighted Least Squares
2.2.2 Maximum Likelihood
2.3 Maximum Likelihood in Multiparameter Exponential Families
2.4 Algorithmic Issues
2.4.1 The Method of Bisection
2.4.2 Coordinate Ascent
2.4.3 The Newton-Raphson Algorithm
2.4.4 The EM (Expectation/Maximization) Algorithm
2.5 Problems and Complements
2.6 Notes
2.7 References
3 MEASURES OF PERFORMANCE
3.1 Introduction
3.2 Bayes Procedures
3.3 Minimax Procedures
3.4 Unbiased Estimation and Risk Inequalities mi ianofT noiciosa or
3.4.1 Unbiased Estimation,Survey Sampling
3.4.2 The Information Inequality I soieiosT 1o moelnngmoD
3.5 Nondecision Theoretic Criteria
3.5.1 Computation
3.5.2 Interpretability
3.5.3 Robustness
3.6 Problems and Complements
3.7 Notes
3.8 References
4 TESTING AND CONFIDENCE REGIONS
4.1 Introduction
4.2 Choosing a Test Statistic: The Neyman-Pearson Lemma
4.3 Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models
4.4 Confidence Bounds, Intervals, and Regions
4.5 The Duality Between Confidence Regions and Tests
4.6 Uniformly Most Accurate Confidence Bounds
4.7 Frequentist and Bayesian Formulations
4.8 Prediction Intervals
4.9 Likelihood Ratio Procedures
4.9.1 Introduction
4.9.2 Tests for the Mean of a Normal Distribution-Matched Pair Experi-ments
4.9.3 Tests and Confdence Intervals for the Difference in Means of Two Normal Populations
4.9.4 The Two-Sample Problem with Unequal Variances
4.9.5 Likelihood Ratio Procedures for Bivariate Normal Distributions
4.10 Problems and Complements
4.11 Notes
4.12 References
5 ASYMPTOTIC APPROXIMATIONS
5.1 Introduction:The Meaning and Uses of Asymptotics
5.2 Consistency
5.2.1 Plug-In Estimates and MLEs in Exponential Family Models
5.2.2 Consistency of Minimum Contrast Estimates
5.3 First-and Higher-Order Asymptotics:The Delta Method with Applications
5.3.1 The Delta Method for Moments
5.3.2 The Delta Method for In Law Approximations
5.3.3 Asymptotic Normality of the Maximum Likelihood Estimate in Exponential Families
5.4 Asymptotic Theory in One Dimension
5.4.1 Estimation:The Multinomial Case
5.4.2 Asymptotic Normality of Minimum Contrast and M-Estimates
5.4.3 Asymptotic Normality and Efficiency of the MLE
5.4.4 Testing
5.4.5 Confidence Bounds
5.5 Asymptotic Behavior and Optimality of the Posterior Distribution
5.6 Problems and Complements
5.7 Notes
5.8 References
6 INFERENCE IN THE MULTIPARAMETER CASE
6.1 Inference for Gaussian Linear Models
6.1.1 The Classical Gaussian Linear Model
6.1.2 Estimation
6.1.3 Tests and Confidence Intervals
6.2 Asymptotic Estimation Theory in p Dimensions
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