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Series Estimation of Regression Functionals

Published online by Cambridge University Press:  11 February 2009

Whitney K. Newey
Whitney K. Newey
Affiliation:
Massachusetts Institute of Technology
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Abstract

Two-step estimators, where the first step is the predicted value from a nonparametric regression, are useful in many contexts. Examples include a non-parametric residual variance, probit with nonparametric generated regressors, efficient GMM estimation with randomly missing data, heteroskedasticity corrected least squares, semiparametric regression, and efficient nonlinear instrumental variables estimators. The purpose of this paper is the development of consistency and asymptotic normality results when the first step is a series estimator. The paper presents the form of a correction term for the first step on the second-step asymptotic variance and gives a consistent variance estimator. Data-dependent numbers of terms are allowed for, and the regressor distribution can be discrete, continuous, or a mixture of the two. Results for several new estimators are given.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 1 , March 1994 , pp. 1 - 28
Copyright
Copyright © Cambridge University Press 1994

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