Min-Max Bias Robust M-Estimates of Scale.
Technical rept. no. 72, 1 Dec 86-30 Nov 87,
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
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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
- Statistics and Probability