Likelihood ratio specification tests

Abstract

Misspecification tests for parametric models, f(y, θ), that examine data for failure of moment conditions implied by the maintained parametric distribution are interpreted as score tests of H0: λ = 0 in the context of a parametric family of distributions r(y; θ, λ). This family contains the maintained distribution as a special case (λ = 0) and has the property that only in that special case do the chosen moment conditions hold. A likelihood ratio test of H0: λ = 0 therefore constitutes an alternative test of the validity of the moment conditions. This test admits a Bartlett correction, unlike conventional moment tests for which adjustments based on second order asymptotic theory may behave b..