Trinmdng the Least Squares Estimator in the Linear R.t>de1 by Using a Preliminary Estimator Trimming the Least Squares Estimator in the Linear Model by Using a Preliminary Estimator

"Let Sn be an estimate of S in the linear model, Y. = x!S + e.. Define the -v 1 -11 residuals Yi xi~' let 0 < a < ~, and let ~ be the least squares estimate of S calculated after removing the observations with the [an] smallest and [an] largest residuals. By use of an asymptotic expansion, the limit distribution of "SL is found under certain regularity conditions. This distribution depends ~ heavily upon the choice Of~. We discuss several choices of ~, with special attention to the contaminated normal model. If ~ is the median regression or "least squares estimator then f L is rather inefficient at the normal model. If F is "symmetric, then a particularly convenient, robust choice is to let ~ equal the average of the ath and (l-a)th regression quantiles (Koenker and Bassett, "Econometrica (1978)). Then ~ has a limit distribution analogous to the trimmed "mean in the location model, and the covariance matrix of ~ is easily estimated.