Some Higher Order Theory for a Consistent Nonparametric Model Specification Test

Abstract

We provide second order theory for a smoothing-based model specification test. We derive the asymptotic cumulants and justify an Edgeworth distributional approximation valid to order close to n^{-1}. This is used to define size-corrected critical values whose null rejection frequency improves on the normal critical values. Our simulations confirm the efficacy of this method in moderate sized samples.Consistent test, Edgeworth expansion, kernel estimation, nonlinear regression