Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models
证明了非参数回归模型中级数估计量的渐近正态性，涵盖傅里叶柔性形式、三角级数和多项式级数估计量，并推广到加性交互、半参数及半参数指数回归模型，适用于同方差或异方差误差。
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 estimates in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskedastic. The paper also considers series estimators for additive interactive regression, semiparametric regression, and semiparametric index regression models, and shows them to be consistent and asymptotically normal. Copyright 1991 by The Econometric Society.