L-Estimation for Linear Models

Analogues of linear-combinations-of-order-statistics, or L-estimators, are suggested for estimating the parameters of the linear regression model.The methods are based on linear combinations of the p-dimensional "regression quantiles" proposed by Koenker and Bassett.A uniform Bahadur-type representation of regression quantiles is established, and this permits a general theory of L-estimators based on regression quantiles including those with smooth weight functions.A leading example of the proposed class of estimators is an analogue of the trimmed mean which seems to exhibit certain advantages over earlier proposals by Koenker and Bassett and Ruppert and Carroll.A brief investigation of two proposals for estimating the covariance matrix of this estimator is also reported.