数理统计(基本思想与重点专题第2卷)(英文版)

数理统计是数学系各专 业的一门重要课程。通过对 某些现象的频率的观察来发 现该现象的内在规律性，并 作出一定精确程度的判断和 预测。数理统计在自然科学 、工程技术、管理科学及人 文社会科学中得到越来越广 泛和深刻的应用。著名统计 学家Bickel 的两卷集《数理 统计：基本思想与专题》。 最近又增加了第2卷，并附 有习题全解。这是一部把大 数据、高维统计融入高等统 计的教材。还包括了当下统 计学的一些热门话题和方法 。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。

PREFACE TO THE 2016 EDITION I INTRODUCTION AND EXAMPLES I.0 Basic Ideas and Conventions I.1 Tests of Goodness of Fit and the Brownian Bridge I.2 Testing Goodness of Fit to Parametric Hypotheses I.3 Regular Parameters.Minimum Distance Estimates I.4 Permutation Tests I.5 Estimation of Irregular Parameters 1.6 Stein and Empirical Bayes Estimation I.7 Model Selection I.8 Problems and Complements I.9 Notes 7 TOOLS FOR ASYMPTOTIC ANALYSIS 7.1 Weak Convergence in Function Spaces 7.1.1 Stochastic Processes and Weak Convergence 7.1.2 Maximal Inequalities 7.1.3 Empirical Processes on Function Spaces 7.2 The Delta Method in Infinite Dimensional Space 7.2.1 Influence Functions.The Gateaux and Frechet Derivatives 7.2.2 The Quantile Process 17.3 Further Expansions 7.3.1 The von Mises Expansion 7.3.2 The Hoeffding and Analysis of Variance Expansions 7.4 Problems and Complements 7.5 Notes 8 BUSTRIBUTION-FREE,UNBIASED,AND EOUIVARIANT PROCEDURES 8.1 Introduction 8.2 Similarity and Completenes 8.2.1 Testing 8.2.2 Testing Optimality Theory 8.2.3 Estimation 8.3 Invariance, Equivariance,and Minimax Procedures 8.3.1 Group Models 8.3.2 Group Models and Decision Theory 8.3.3 Characterizing Invariant Tests 8.3.4 Characterizing Equivariant Estimates 8.3.5 Minimaxity for Tests:Application to Group Models 8.3.6 Minimax Estimation,Admissibility,and Steinian Shrinkage 8.4 Problems and Complements 8.5 Notes 9 INFERENCE IN SEMIPARAMETRIC MODELS 9.1 Estimation in Semiparametric Models 9.1.1 Selected Examples 9.1.2 Regularization.Modified Maximum Likelihood 9.1.3 Other Modified and Approximate Likelihoods 9.1.4 Sieves and Regularization 9.2 Asymptotics.Consistency and Asymptotic Normality 9.2.1 A General Consistency Criterion 9.2.2 Asymptotics for Selected Models 9.3 Efficiency in Semiparametric Models