LIMIT-THEOREMS FOR THE SIMPLICIAL DEPTH

被引：34

作者：

DUMBGEN, L ^{[1
]}

机构：

[1] INST ANGEW MATH,INF 294,W-6900 HEIDELBERG,GERMANY

来源：

STATISTICS & PROBABILITY LETTERS | 1992年 / 14卷 / 02期

关键词：

SIMPLICIAL DEPTH; VAPNIK-CERVONENKIS CLASS; EMPIRICAL PROCESS; ROBUSTNESS; MULTIVARIATE L-STATISTIC;

D O I：

10.1016/0167-7152(92)90075-G

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：

The large sample behavior and a robustness property of the simplicial depth for multivariate data, introduced by R. Liu (1990), are studied. A functional CLT is derived and applied to an L-statistic, which estimates the center of a smooth symmetric distribution on d-dimensional Euclidean space.

引用

页码：119 / 128

页数：10

共 6 条

[1]

ARCONES MA, 1991, UNPUB LIMIT THEOREMS

[2] UNIFORMITY IN WEAK CONVERGENCE [J].

BILLINGS.P ;

TOPSOE, F .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1967, 7 (01) :1-&

[3]

DUMBGEN L, 1990, 581 U HEID PREPR

[4] A CLASS OF STATISTICS WITH ASYMPTOTICALLY NORMAL DISTRIBUTION [J].

HOEFFDING, W .

ANNALS OF MATHEMATICAL STATISTICS, 1948, 19 (03) :293-325

[5] ON A NOTION OF DATA DEPTH BASED ON RANDOM SIMPLICES [J].

LIU, RY .

ANNALS OF STATISTICS, 1990, 18 (01) :405-414

[6]

Pollard D., 1984, CONVERGENCE STOCHAST

← 1 →