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Discussion Paper

Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models

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.