Consistent Specification Testing via Nonparametric Series Regression.

This paper proposes two consistent one-sided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. The authors estimate the nonparametric model by series regression. The new test statistics converge in distribution to a unit normal under correct specification and grow to infinity faster than the parametric rate [square root of] n under misspecification, while avoiding weighting, sample splitting, and nonnested testing procedures used elsewhere. Copyright 1995 by The Econometric Society.