稳健估计和检验的若干进展  

Some Recent Developments on Robust Estimation and Tests

作　　者：张健[1] 李国英[1] 

机构地区：[1]中国科学院系统科学研究所

出　　处：《数学进展》1998年第5期403-415,共13页Advances in Mathematics（China）

摘　　要：本文介绍近几年在稳健估计和稳健检验方面的若干进展，包括：（１）一维位置Ｍ估计的崩溃点，特别是重降Ｍ估计的样本崩溃点的渐近性质；（２）多元位置和散布阵的ＰＰ型估计及其性质；（３）统计检验的崩溃点，以及ｔ检验、Ｔ２检验、Ｍ检验、得分检验、ｘ２检验等一些常用检验方法的崩溃稳健性．此外，本文还简要叙述了稳健性的基本概念以及上述三方面的主要理论．This paper gives a veviw of some new developments on robust estimation and tests in recent years, including: (1) breakdown properties of M-estimators for one-dimenssional location,in particular, the asymptotic properties of sample breakdown points of redescending M-estimators; (2) PP type estimators for multivariate location and dispersion matrices and their properties; (3) the breakdown points of statistical tests, and breakdown properties of t-test, T 2-test, M-test, score test and X 2-test etc. Also, basic concepts of robustness and main theory of the above three topics are briefly introduced.

关 键 词：样本崩溃点 重降M估计 稳健检验 稳健估计 

分 类 号：O212.1[理学—概率论与数理统计] O211.67[理学—数学]