COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 874R

"Asymptotic Normality of Series Estimators
for Various Nonparametric and Semiparametric Models"

Donald W. K. Andrews

May 1988
Revised June 1989

This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant's Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskeclastic. The paper also considers series estimators for additive interactive regression (AIR), seimparametric regression, and semiparametric index regression models and shows them to be consistent and asymptotically normal. All of the consistency and asymptotic normality results in the paper follow from one set of general results for series estimators.

JE Classification: 211

Keywords: Asymptotic normality, nonparametric regression, polynomial series, semiparametric regression, series estimators