The tail behavior of the least-squares estimator in the linear regression model was studied in He et al. (Econometrica 58 (1990) 1195) under a fixed design for finite n. We now consider a random design matrix Xn and the case n--[infinity] and study the probability with [gamma]n=F-1(1-1/n), a...

We consider a simple through-the-origin linear regression example introduced by Rousseeuw, van Aelst and Hubert (J. Amer. Stat. Assoc., 94 (1994) 419-434). It is shown that the conventional least squares and least absolute error estimators converge in distribution without normalization and...