ASPECTS OF ROBUST LINEAR-REGRESSION

被引:64
作者
DAVIES, PL
机构
关键词
INFLUENCE FUNCTION; LIPSCHITZ CONTINUITY; GLOBAL DEFINABILITY; BREAKDOWN POINT; LINEAR EQUIVARIANCE;
D O I
10.1214/aos/1176349401
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
Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that S-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of the Krasker-Welsch dispersion functional is obtained as well as bounds for the corresponding regression functional. Section 6 contains the construction of a linearly equivariant, high breakdown and locally Lipschitz dispersion functional for any design distribution. In Section 7 it is shown that there is no inherent contradiction between efficiency and a high breakdown point. Section 8 contains a linearly equivariant, high breakdown regression functional which is Lipschitz continuous at models with normal errors.
引用
收藏
页码:1843 / 1899
页数:57
相关论文
共 48 条
[21]   EFFICIENT BOUNDED-INFLUENCE REGRESSION ESTIMATION [J].
KRASKER, WS ;
WELSCH, RE .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1982, 77 (379) :595-604
[22]   ESTIMATION IN LINEAR-REGRESSION MODELS WITH DISPARATE DATA POINTS [J].
KRASKER, WS .
ECONOMETRICA, 1980, 48 (06) :1333-1346
[24]   BREAKDOWN POINTS OF AFFINE EQUIVARIANT ESTIMATORS OF MULTIVARIATE LOCATION AND COVARIANCE MATRICES [J].
LOPUHAA, HP ;
ROUSSEEUW, PJ .
ANNALS OF STATISTICS, 1991, 19 (01) :229-248
[25]   ROBUST M-ESTIMATORS OF MULTIVARIATE LOCATION AND SCATTER [J].
MARONNA, RA .
ANNALS OF STATISTICS, 1976, 4 (01) :51-67
[26]   ASYMPTOTIC-BEHAVIOR OF GENERAL M-ESTIMATES FOR REGRESSION AND SCALE WITH RANDOM CARRIERS [J].
MARONNA, RA ;
YOHAI, VJ .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1981, 58 (01) :7-20
[27]   THE BREAKDOWN POINT OF SIMULTANEOUS GENERAL M-ESTIMATES OF REGRESSION AND SCALE [J].
MARONNA, RA ;
YOHAI, VJ .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1991, 86 (415) :699-703
[28]  
MARONNA RA, 1979, SMOOTHING TECHNIQUES, P91
[29]  
Morgenthaler S., 1989, J AM STAT ASSOC, V84, P636
[30]   THE EXCESS-MASS ELLIPSOID [J].
NOLAN, D .
JOURNAL OF MULTIVARIATE ANALYSIS, 1991, 39 (02) :348-371