Discussion of the paper “ Inference for Semiparametric Models : Some Questions and an Answer ” by Bickel and Kwon ∗

Bickel and Kwon are to be congratulated for this neat, insightful and stimulating paper on the general theory of semiparametric efficiency and for their successfully posing several important and challenge questions on semiparametric inferences. Semiparametric parametric models arise frequently in many applications. The interest in estimating certain principal parameters while imposing few assumptions on nuisance parameters gives rise to semiparametric models. The parameters of interest usually admit the similar interpretations to those in parametric models. Most of work focuses on efficient inferences on parameters of interest when semiparametric models are correctly specified. The question arises naturally how to validate whether a semiparametric model fits a given set of data, as asked by Bickel and Kwon. I welcome the opportunity to make a few comments and to provide additional insights.