Finite sample tail behavior of multivariate location estimators

被引:4
作者
Zuo, YJ
机构
[1] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
[2] Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA
关键词
breakdown point; data depth; halfspace median; monotonicity; multivariate L-estimators; robustness; tail behavior;
D O I
10.1016/S0047-259X(02)00059-3
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
A finite sample performance measure of multivariate location estimators is introduced based on "tail behavior". The tail performance of multivariate "monotone" location estimators and the halfspace depth based "non-monotone" location estimators including the Tukey halfspace median and multivariate L-estimators is investigated. The connections among the finite sample performance measure, the finite sample breakdown point, and the halfspace depth are revealed. It turns out that estimators with high breakdown point or halfspace depth have "appealing" tail performance. The tail performance of the halfspace median is very appealing and also robust against underlying population distributions, while the tail performance of the sample mean is very sensitive to underlying population distributions. These findings provide new insights into the notions of the halfspace depth and breakdown point and identify the important role of tail behavior as a quantitative measure of robustness in the multivariate location setting. (C) 2003 Elsevier Science (USA). All rights reserved.
引用
收藏
页码:91 / 105
页数:15
相关论文
共 27 条
[1]  
ANTOCH J, 1984, ROBUSTNESS STAT METH
[2]  
ANTOCH J, 1984, P 3 PRAG S AS STAT, P185
[3]   RATES OF CONVERGENCE OF ESTIMATES AND TEST STATISTICS [J].
BAHADUR, RR .
ANNALS OF MATHEMATICAL STATISTICS, 1967, 38 (02) :303-&
[4]   BREAKDOWN PROPERTIES OF LOCATION ESTIMATES BASED ON HALF-SPACE DEPTH AND PROJECTED OUTLYINGNESS [J].
DONOHO, DL ;
GASKO, M .
ANNALS OF STATISTICS, 1992, 20 (04) :1803-1827
[5]  
DONOHO DL, 1983, FESTSCHRIFT EL LEHMA, P157
[6]   RATE OF CONVERGENCE OF CONSISTENT POINT ESTIMATORS [J].
FU, JC .
ANNALS OF STATISTICS, 1975, 3 (01) :234-240
[7]  
HE X, 1998, APPL STAT SCI, V3, P71
[8]   TAIL BEHAVIOR OF REGRESSION-ESTIMATORS AND THEIR BREAKDOWN POINTS [J].
HE, XM ;
JURECKOVA, J ;
KOENKER, R ;
PORTNOY, S .
ECONOMETRICA, 1990, 58 (05) :1195-1214
[9]  
He XM, 1997, ANN STAT, V25, P495
[10]   ROBUST CONFIDENCE LIMITS [J].
HUBER, PJ .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1968, 10 (04) :269-&