
Accession Number : ADA191345
Title : MinMax Bias Robust Regression.
Descriptive Note : Technical rept.,
Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
Personal Author(s) : Martin, R D ; Yohai, V J ; Zamar, R H
PDF Url : ADA191345
Report Date : Aug 1987
Pagination or Media Count : 40
Abstract : This paper considers the problem of minimizing the maximum asymptotic bias of regression estimates over epsiloncontamination neighborhoods for the joint distribution of the response and carriers. Two classes of estimates are treated: (1) Mestimates with bounded function rho applied to the scaled residuals, using a very general class of scale estimates, and (2) Bounded influence function type generalized Mestimates. Estimates in the first class are obtained as the solution of a minimization problem, while estimates in the second class are specified by an estimating equation. The first class of Mestimates is sufficiently general to include both Huber Proposal 2 simultaneous estimates of regression coefficients and residuals scale, and RousseeuwYohai Sestimates of regression. It is shown than an Sestimate based on a jumpfunction type rho solves the minmax bias problem for the class of Mestimates with very general scale. This estimate is obtained by the minimization of the alphaquantile of the squared residuals, where alpha=(epsilon) depends on the fraction of contamination epsilon. When epsilon approaches limit of .5, alpha (epsilon) approaches limit of .5 and the minmax estimator approaches the least median of squared residuals estimator introduced by Rousseeuw. For the bounded influence class of GMestimates, it is shown the a sign type nonlinearity yields the minmax estimate. This estimate coincides with the minimum grosserror sensitivity GMestimate.
Descriptors : *ESTIMATES, *REGRESSION ANALYSIS, COEFFICIENTS, DISTRIBUTION, EQUATIONS, RESIDUALS, SCALE, BIAS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE