ASYMPTOTICS FOR MULTIVARIATE TRIMMING

被引：43

作者：

NOLAN, D

机构：

[1] University of California at Berkeley, CA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1992年 / 42卷 / 01期

基金：

美国国家科学基金会;

关键词：

ROBUST ESTIMATION; RANDOM SET; EMPIRICAL PROCESS; WEAK CONVERGENCE; CUBE-ROOT RATE OF CONVERGENCE;

D O I：

10.1016/0304-4149(92)90032-L

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

One version of multivariate trimming is the operation that intersects all halfspaces with probability content 1 - alpha or greater. The result is a alpha-trimmed convex set, and this set is stochastic when the empirical distribution of a sample determines the probability content of the halfspaces. In this paper, conditions are found for the weak convergence of the boundary of this set to a Gaussian process. It is also shown that an n1/3 normalization produces a limit distribution for the direction normal to the boundary of the set. Intuitive geometric arguments and empirical process methods are employed to establish both limit results.

引用

页码：157 / 169

页数：13

共 14 条

[1] RATES OF GROWTH AND SAMPLE MODULI FOR WEIGHTED EMPIRICAL PROCESSES INDEXED BY SETS [J].

ALEXANDER, KS .

PROBABILITY THEORY AND RELATED FIELDS, 1987, 75 (03) :379-423

[2]

[Anonymous], 1972, ROBUST ESTIMATES LOC

[3] ORDERING OF MULTIVARIATE DATA [J].

BARNETT, V .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY, 1976, 139 :318-354

[4]

CHERNOFF H, 1964, ANN I STAT MATH, V146, P31

[5]

Donoho D.L., 1982, BREAKDOWN PROPERTIES

[6]

DONOHO DL, 1987, 133 U CAL DEP STAT T

[7]

HAMPEL FR, 1986, ROBUST STATISTICS AP

[8] CUBE ROOT ASYMPTOTICS [J].

KIM, JY ;

POLLARD, D .

ANNALS OF STATISTICS, 1990, 18 (01) :191-219

[9]

Marcus MB., 1981, RANDOM FOURIER SERIE

[10]

NATH GB, 1971, APPL STAT, V20, P313

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