统计学中的渐近性

统计学中的渐近性:基本概念(第2版)(英文)》是第2版，第1版条理地介绍了渐近统计学近50年来的发展。第2版与第1版的不同之处在于它对读者更加“友好”。其中也包括一个新的章节，第4章，关于Gaussian 和Poisson试验，它在统计学的研究领域发挥着越来越重要的作用，尤其在非参数和半参数学中。接下来的大部分章节全部都重写了，对第7章中的非参数学进行了更详细的叙述。

Dedicatory Note Preface to the Second Edition Preface to the First Edition 1 Introduction 2 Experiments， Deficiencies， Distances 2.1 Comparing Risk Functions 2.2 Deficiency and Distance between Experiments 2.3 Likelihood Ratios and Blackwell's Representation 2.4 Further Remarks on the Convergence of Distributions of Likelihood Ratios 2.5 Historical Remarks 3 Contiguity—Hellinger Transforms 3.1 Contiguity 3.2 Hellinger Distances， Hellinger Transforms 3.3 Historical Remarks 4 Gaussian Shift and Poisson Experiments 4.1 Introduction 4.2 Gaussian Experiments 4.3 Poisson Experiments 4.4 Historical Remarks 5 Limit Laws for Likelihood Ratios 5.1 Introduction 5.2 Auxiliary Results 5.2.1 Lindeberg's Procedure 5.2.2 Levy Splittings 5.2.3 Paul Levy's Symmetrization Inequalities 5.2.4 Conditions for Shift—Compactness 5.2.5 A Central Limit Theorem for Infinitesimal Arrays 5.2.6 The Special Case of Gaussian Limits 5.2.7 Peano Differentiable Functions 5.3 Limits for Binary Experiments 5.4 Gaussian Limits 5.5 Historical Remark 6 Local Asymptotic Normality 6.1 Introduction 6.2 Locally Asymptotically Quadratic Families 6.3 A Method of Construction of Estimates 6.4 Some Local Bayes Properties 6.5 Invariance and Regularity 6.6 The LAMN and LAN Conditions 6.7 Additional Remarks on the LAN Conditions 6.8 Wald's Tests and Confidence Ellipsoids 6.9 Possible Extensions 6.10 Historical Remarks 7 Independent， Identically Distributed Observations 7.1 Introduction 7.2 The Standard i.i.d.Case： Differentiability in Quadr Mean 7.3 Some Examples 7.4 Some Nonparametric Considerations 7.5 Bounds on the Risk of Estimates 7.6 Some Cases Where the Number of Observations Is Random 7.7 Historical Remarks 8 On Bayes Procedures 8.1 Introduction 8.2 Bayes Procedures Behave Nicely 8.3 The Bernstein—von Mises Phenomenon 8.4 A Bernstein—von Mises Result for the i.i.d.Case 8.5 Bayes Procedures Behave Miserably 8.6 Historical Remarks Bibliography Author Index Subject Index

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