Statistica Sinica 7(1997), 669-686

AN EFFICIENT CLASS OF WEIGHTED TRIMMED MEANS

FOR LINEAR REGRESSION MODELS

Lin-An Chen

National Chiao Tung University

Abstract: We propose and study a class of weighted trimmed means based on the symmetric q uantile functions for the location and linear regression models. A robustness compariso n with the underlying distribution of a symmetric-type heavy tail is given. The weighted trimmed mean in optimal trimming under symmetric distributions is shown to have an asymptotic variance very close to the Cramér-Rao lower bound. For fixed weight setting, the weighted trimmed mean is still relatively more efficient in terms of asymptotic variance than the trimme d mean based on regression quantiles. From the parametric point of view, the comp utationally easy weighted trimmed mean is shown to be an efficient alternative to maximum likelihood estimation which is usually computationally difficult for most underlying distributions except the ideal case of normal ones. From the nonparametric point of view, this weighted trimmed mean is shown to be an effic ient alternative robust estimator. A methodology for confidence ellipsoids and hypothesis testing based on the weighted trimmed mean is also introduced.

Key words and phrases: Initial estimator, symmetric quantile, weighted trimmed mean.