Lucien Le Cam 是伯克利的加利福尼亚大学的统计与数学专业的教授。Grace Lo Yang是科利奇帕克马利兰大学数学学院的教授。
目錄：
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
內容試閱：
We shall return later to the relations between the LAQ conditions and the convergence of experiments described in Chapters 3 and 5.For now， we shall describe a method of construction of centering variables Zn that， together with estimates of the matrices Kn， will have asymptotic sufficiency properties.It is based on the relations between differences of log likelihood described in （6.1） above.
6.3 A Method of Construction of Estimates
For each integer n.， consider an experiment εn={Pθ，n；θ∈θ}where e is a subset of a euclidean space Rk.It often happens that the statistician has available some auxiliary estimate θn that indicates in what range θ is likely to be.The question might then be how to use this 0： to get a better summary of the information available in the experiment， as well as a possibly better estimate.Here we describe some properties of a method that yields， under the LAQ conditions， estimates with asymptotic optimality properties.See， Proposition 3 and Section 6.4 on Bayes procedures.The method amounts to the following： Fit a quadratic to the log likelihood around the estimated value 0* and take as the new estimated value of θ the point that maximizes the fitted quadratic.To ensure that the method works，we shall use two assumptions； the first says that θ*n puts you iu the right neighborhood.
購物車/收銀台(0) | 在線留言板
| 付款方式
| 運費計算
| 聯絡我們
| 幫助中心 |
加入書簽
HOME
新書上架
