Min-Max Bias Robust M-Estimates of Scale

摘要

Min-max bias robust M-estimates of scale are obtained for positive random variables which have epsilon-contamines distributions. Any such estimate a scaled order statistic, with the order statistic determined by epsilon. As epsilon approached 0.5 the min-max bias robust estimate 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 ween 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 centering data, with the median as the centering estimate. This esitamte is extremely close to a scaled median absolute deviation about the median, in terms of both structure and bias behavior. (Author)