COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1106

"Testing Additivity in Generalized Nonparametric Regression Models"

Pedro Gozalo and Oliver Linton

July 1995
Revised February 1997

We develop kernel-based consistent tests of an hypothesis of additivity in nonparametric regression extending recent work on testing parametric null hypotheses against nonparametric alternatives. The additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for standard estimators. The asymptotic distributions of the tests under a sequence of local alternatives are found and compared: in fact, we give a ranking of the different tests based on local asymptotic power. The practical performance is investigated via simulations and an application to the German migration data of Linton and Härdle (1996).

Keywords: Additive regression models, Dimensionality reduction, Kernel estimation, Nonparametric regression, Testing

JEL Classification: C12, C13

Old title: "A Nonparametric Test of Conditional Independence"