Estimating the variance of the LAD regression coefficients

The covariance matrix of the regression coefficients in LAD depends upon the density of the errors at the median. This requires distributional assumptions which are not needed to estimate the regression coefficients and which can cause misspecification. To avoid distributional assumptions, we present a covariance matrix estimator based on the variability of the coefficients exactly computed over all the possible k-dimensional subsets, where k is the number of explanatory variables. The estimator turns out to be useful with contaminated distributions and non-i.i.d. errors. It is a particular version of the jackknife variance estimator, where the pseudo-values are exactly computed in each subset. A Monte-Carlo study analyses its behavior in small samples. (C) 1998 Elsevier Science B.V. All rights reserved.