Divergence and Model Adequacy, a Semiparametric Case Study

Adequacy for estimation between an inferential method and a model can be defined through two main requirements: firstly the inferential tool should define a well posed problem when applied to the model; secondly the resulting statistical procedure should produce consistent estimators. Conditions which entail these analytical and statistical issues are considered in the context when divergence based inference is applied for smooth semiparametric models under moment restrictions. A discussion is also held on the choice of the divergence, extending the classical parametric inference to the estimation of both parameters of interest and of nuisance.Classical arguments in favor of the omnibus choice of the L2 and Kullback Leibler divergences are discussed and motivation for the class of power divergences is presented in the context of the present semi parametric smooth models. A short simulation study illustrates the method.