Divergence and Model Adequacy, A Semiparametric Case Study

TL;DR

This paper investigates divergence-based inference in smooth semiparametric models under moment restrictions, focusing on model adequacy, divergence choice, and extending classical parametric inference with a simulation study.

Contribution

It provides conditions for model adequacy and introduces a framework for divergence choice in semiparametric inference, extending classical methods to include nuisance parameter estimation.

Findings

L2 and Kullback-Leibler divergences are recommended for omnibus inference.

The paper extends classical parametric inference to semiparametric models.

A simulation study demonstrates the practical application of the proposed methods.

Abstract

Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne 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. Arguments in favor of the omnibus choice of the L 2 and Kullback Leibler choices as presented in [16] are discussed and motivation for the class of power divergences de{\ldots}ned in [5] is presented in the context of the present semi parametric smooth models. A short simulation study illustrates the method.