Min-Max Bias Robust M-Estimates of Scale.
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 approaches limit of 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 = (epsilon)sub 0 + 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1986
- Accession Number
- ADA179255
Entities
People
- R. D. Martin
- Ruben H. Zamar
Organizations
- University of Washington