Accession Number : ADA180127

Title :   Min-Max Bias Robust M-Estimates of Scale.

Descriptive Note : Technical rept. no. 72, 1 Dec 86-30 Nov 87,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF STATISTICS

Personal Author(s) : Martin,R D ; Zamar,Ruben H

PDF Url : ADA180127

Report Date : Dec 1986

Pagination or Media Count : 39

Abstract : Min-max bias robust M-estimates of scale are obtained for positive random variables which have epsilon-contaminated distributions. Any such estimate is a scaled order statistic, with the order statistic determined by epsilon. As epsilon approached 0.5 the min-max bias robust estimate becomes a scaled sample median, which thereby enjoys both high breakdown point of 0.5 and min-max bias robustness. Furthermore, for a wide range of epsilon, min-max estimate is quite close to the scaled median in terms of both structure and min-max bias behavior. Results are also obtained for random variables whose distribution is F = (1 - epsilon) F sub o + epsilon H with F sub o symmetric about an unknown location parameter. In particular we show that when F sub o is normal and or = epsilon or = .35, the min-max bias M-estimate of scale is a scaled order statistic applied to the absolute value of centered data, with the median as the centering estimate. This estimate is extremely close to a scaled median absolute deviation about the median, in terms of both structure and bias behavior. (Author)

Descriptors :   *ESTIMATES, *SCALE, *ORDER STATISTICS, BEHAVIOR, BIAS, RANDOM VARIABLES, RANGE(EXTREMES)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE