COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1148

Some Higher Order Theory for a
Consistent Nonparametric Model Specification Test

Yanqin Fan and Oliver Linton

February 1997

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.