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Convergence rates and asymptotic normality for series estimators. (English) Zbl 0873.62049
Summary: 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 $$\sqrt{n}$$-consistency 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.

##### MSC:
 62G20 Asymptotic properties of nonparametric inference 62G07 Density estimation 62P20 Applications of statistics to economics 62J02 General nonlinear regression
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