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September, 1993 On Efficient Estimation in Regression Models
Anton Schick
Ann. Statist. 21(3): 1486-1521 (September, 1993). DOI: 10.1214/aos/1176349269


In this paper we consider the regression model with smooth regression function and smooth error and covariate distributions. We study how well one can estimate functionals of the regression function which may also depend on the distribution of the covariate. This is done by deriving the efficient influence functions of least dispersed regular estimators of such functionals under various assumptions on the parameters of our model. Then we demonstrate how efficient estimates can be constructed. We provide a general procedure for constructing efficient estimates that relies on appropriate auxiliary estimates. We illustrate the usefulness of this procedure by constructing efficient estimates for various parametric, nonparametric and semiparametric models.


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Anton Schick. "On Efficient Estimation in Regression Models." Ann. Statist. 21 (3) 1486 - 1521, September, 1993.


Published: September, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0807.62035
MathSciNet: MR1241276
Digital Object Identifier: 10.1214/aos/1176349269

Primary: 62G20
Secondary: 62G05

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 3 • September, 1993
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