Symmetric quantile and symmetric trimmed mean for linear regression model

Abstract

We propose and investigate an initial estimator-based “symmetrized” quantile function, and a trimmed mean based on this quantile function for linear regression model. This symmetric trimmed mean provides a generalization of the metrically trimmed mean by Kim (1992) to an estimation of regression parameters. The symmetric trimmed mean is compared with Koenker and Bassett's (1978) trimmed mean in terms of asymptotic variances under symmetric and asymmetric error distributions. Under optimal trimming and symmetric error, the symmetric trimmed mean is shown not only more efficient than the Koenker and Bassett's trimmed mean, but also has asymptotic variance as small as the Cramer-Rao lower bound when the contaminated variance goes to infinity.