Abstract
We survey the asymptotic properties of regression Lp estimators under general classes of error distributions. It is found that the asymptotic distributions of Lp estimators depend crucially on p and the shape of the error distribution near the origin. A number of important features arise as a result, among which are (a) use of a small p may yield accelerated convergence rates for Lp estimators under certain classes of error distributions; (b) for p < 1, Lp regression should, under some circumstances, be undertaken by locally maximizing, rather than minimizing, the sum of the pth powers of the absolute deviations; and (c) consistent estimation of the sampling distributions of the Lp estimators can be achieved by the m out of n bootstrap in general. Numerical examples are provided to illustrate our theoretical findings, and a computational algorithm is suggested for local maximization as may sometimes be required by the Lp procedure.
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