A Shortcut to LAD Estimator Asymptotics
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justiﬁed by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with ﬁxed and random regressors, autoregressions and autoregressions with inﬁnite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator and the results of some earlier simulation studies are examined.
Phillips, Peter C.B., "A Shortcut to LAD Estimator Asymptotics" (1990). Cowles Foundation Discussion Papers. 1192.