Sub-sampling and weighting approaches to model checking

Abstract

Motivated by the ideas of sub-sampling and sample splitting, we propose a weighting approach to model checking that exploits the systematic differences under model misspecification between the weighted, the complementarily weighted and the unweighted parameter estimates. Standard error formulae for the differences are derived and the resulting standardized differences can be used to test the adequacy of the postulated model. Unlike many tests in the literature that are designed to test the goodness of fit of a particular class of models such as logistic regression, the proposed approach is very general and can be implemented easily to test the goodness of fit of any parametric model.