Bias Robust Estimation of Scale Where Location Is Unknown
نویسندگان
چکیده
In this paper we consider the problem of robust estimation of the scale of the location residuals when the "true" underlying distribution of the data belongs to a contamination neighborhood of a parametric location-scale family. First we show that a scaled version of the l\tlADAM (median of absolute residuals about the median) is approximately most bias-robust within the class 0 Huber's proposal II joint estimates of location and scale. Then we consider the larger class of M-estimates of scale with general location and show that a scaled version of the SHORTH (the shortest half of the data) is approximately most bias-robust in this case. The exact min-max asymptotic bias estimate is a scaled order statistic of the residuals about a certain location estimate. The exact order, scaling and location depend on the fraction of contamination, loss function we present a HLIJIH,,", Bias Robust Estimation of Scale When Location Is Unknown
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