《統計學中的漸近性：基本概念（第2版）》是2015年世界圖書出版公司出版的著作，作者是[美] Lucien Le Cam（L.L.卡姆）。
基本介紹
- 書名：《統計學中的漸近性：基本概念（第2版）》
- 作者：[美] Lucien Le Cam（L.L.卡姆）
- 出版社：世界圖書出版公司
- 出版時間：2015年10月01日
內容簡介,作者簡介,目錄,
內容簡介
該卷是第2版，第請棄1版條理地介紹了漸近統計學近50年來的發展。第2版與第1版的不同之處在於它對讀者刪連嚷更加“友好”。其中也包括一個新的章蒸詢嚷龍節，第4章，關於Gaussian 和Poisson試驗，它在統計學的研究領域發揮著越來越重要的作用，槓漏肯尤其道只樂在非參數和半參數學中。接下來的大部分章節全部都重寫了，對第7章中的非參數學進行了更詳細的敘述。
作者簡介
Lucien Le Cam 是伯克利的加利福尼亞大學的統計與數學專業的教授。Grace Lo Yang是科利奇帕克奔定墓馬里蘭大學數學學院的教授。
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，恥巴汗喇 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
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
