Asymptotic Optimality of Empirical Likelihood for Selecting Moment Restrictions

This paper proposes large deviation optimal properties of the empirical likelihood testing (ELT) moment selection procedures for moment restriction models. Since the parameter spaces of the moment selection problem is discrete, the conventional Pitman-type local alternative approach is not very helpful. By applying the theory of large deviations, we analyze convergence rates of the error probabilities under some …xed distribution. We propose three optimality results for the ELT procedures: (i) the generalized Neyman-Pearson optimality under …xed critical values, (ii) a modi…ed version of the generalized Neyman-Pearson optimality under decreasing critical values, and (iii) the minimax misclassi…cation error optimality. By comparing the convergence rates of the error probabilities, we can evaluate moment selection procedures beyond the consistency.