
Accession Number : ADA180127
Title : MinMax Bias Robust MEstimates of Scale.
Descriptive Note : Technical rept. no. 72, 1 Dec 8630 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 : Minmax bias robust Mestimates of scale are obtained for positive random variables which have epsiloncontaminated distributions. Any such estimate is a scaled order statistic, with the order statistic determined by epsilon. As epsilon approached 0.5 the minmax bias robust estimate becomes a scaled sample median, which thereby enjoys both high breakdown point of 0.5 and minmax bias robustness. Furthermore, for a wide range of epsilon, minmax estimate is quite close to the scaled median in terms of both structure and minmax 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 minmax bias Mestimate 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