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The hiweight is one member of the family of M-estimators used to estimate location. The variance of this estimator is calculated via Monte Carlo simulation for samples of sizes 5, 10, and 20. The scale factors and tuning constants used in the definition of the biweight are varied to determine their effects on the variance. A measure of efficiency for three distributional situations (Gaussian and two stretched-tailed distributions) is determined. Using a biweight scale and a tuning constant of c = 6, the biweight attains an efficiency of 98.2% for samples of size 20 from the Gaussian distribution. The minimum efficiency at n = 20 using the biweight scale and c = 4 is 84..%, revealing that the biweight performs well even when the underlying distibution of the samples has abnormauly stretched tails.
Karen Kafadar (Tue,) studied this question.