Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications
This paper and its sequel, Andrews , extend the Pearson chi-square testing method to non-dynamic parametric econometric models, in particular, models with covariates. The present paper introduced the test and discusses a wide variety of applications. Andrews  establishes the asymptotic properties of the test, by extending recent probabilistic results for the weak convergence of empirical processes indexed by sets. The chi-square test that is introduced can be used to test goodness-of-ﬁt of a parametric model, as well as to test particular aspects of the parametric model that are of interest. In the event of rejection of the null hypothesis of correct speciﬁcation, the test provides information concerning the direction of departure from the null. The results allow for estimation of the parameters of the model by quite general methods. The cells used to construct the test statistic my be random and can be speciﬁed in a general form.
Andrews, Donald W.K., "Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications" (1985). Cowles Foundation Discussion Papers. 1003.