Efficiency in Asymptotic Shift Experiments∗

This paper generalizes classical results on efficient point estimation in parametric models. The asymptotic optimality of maximum likelihood estimators is, generally, tied to both the regularity of the statistical model and symmetry of the loss function in the efficiency criterion. We examine the possibility of locally shifting or “bias-correcting” the MLE to achieve efficiency. In parametric models which asymptotically have a full shift form, including local asymptotic normal models, a feasible locally shifted MLE is optimal. ∗We are grateful to Gary Chamberlain, Thomas Rothenberg, Peter Bickel, and numerous seminar participants for comments. We thank the National Science Foundation for research support under grants SES-9985257 (Hirano) and SES-0112095 (Porter).