Determination of Estimators with Minimum Asymptotic Covariance Matrices

We give a straightforward condition sufficient for determining the minimum asymptotic variance estimator in certain classes of estimators relevant to econometrics. These classes are relatively broad, as they include extremum estimation with smooth or nonsmooth objective functions; also, the rate of convergence to the asymptotic distribution is not required to be <italic>n</italic>^−½. We present examples illustrating the content of our result. In particular, we apply our result to a class of weighted Huber estimators, and obtain, among other things, analogs of the generalized least-squares estimator for least <italic>L</italic>_null-estimation, 1 ≤ <italic>p</italic> < ∞.