Asymptotic efficiency in parametric structural models with parameter-dependent support

In certain auction, search and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standards asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constructing efficient point estimators. We show that the maximum likelihood estimators is generally inefficient, but that the Bayes estimator is efficient according to the local asymptotic minimax criterion for conventional loss functions. We provide intuition for this result using Le Cam's limits of experiments framework.