Convergence rates and asymptotic normality for series estimators

Abstract

This paper gives general conditions for convergence rates and asymptotic normality of series estimators of conditional expectations, and specializes these conditions to polynomial regression and regression splines. Both mean-square and uniform convergence rates are derived. Asymptotic normality is shown for nonlinear functionals of series estimators, covering many cases not previously treated. Also, a simple condition for n-consitency of a functional of a series estimator is given. The regularity conditions are straightforward to understand, and several examples are given to illustrate their application.