A remark on approximate M-estimators

An approximate M-estimator is defined as a value that minimizes certain random function up to a [var epsilon]n, where {[var epsilon]n} is a sequence of real numbers converging to zero. We determine the rate of [var epsilon]n so that the approximate M-estimator is asymptotically normal with rate n1/2. Our results apply to common M-estimators such as the least absolute deviations estimator for the linear model.M-estimators LAD regression