Diagnostic testing and evaluation of maximum likelihood models

Abstract

The paper develops a unified theory of likelihood specification testing based on M-estimators of auxiliary parameters. The theory is sufficiently general to encompass a wide class of specification tests including moment-based tests, Pearson-type goodness of fit tests, the information matrix test, and the Cox test. The paper also presents a framework based on Frechet differentiation for determining the effects of misspecification on the almost sure limits of parameter estimates and specification test statistics. © 1985.