On Some Analogues to Linear Combinations of Order Statistics in the Linear Model

Abstract

We consider the general linear model with independent symmetric errors. In this context we propose and examine the large sample behavior of some estimates of the regression parameters. For the location model these statistics are linear combinations of order statistics. In general they depend on a preliminary estimate and the ordered residuals based on it. The asymptotic efficiency of these procedures is independent of the design matrix. Specifically analogues of the median and trimmed and Winsorized means are proposed.