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October 1999 Estimation in a semiparametric partially linear errors-in-variables model
Hua Liang, Wolfgang Härdle, Raymond J. Carroll
Ann. Statist. 27(5): 1519-1535 (October 1999). DOI: 10.1214/aos/1017939140

Abstract

We consider the partially linear model relating a response $Y$ to predictors ($X, T$) with mean function $X^{\top}\beta + g(T)$ when the $X$’s are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter $\beta$ and the function $g(\cdot)$ when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of $\beta$ is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.

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Hua Liang. Wolfgang Härdle. Raymond J. Carroll. "Estimation in a semiparametric partially linear errors-in-variables model." Ann. Statist. 27 (5) 1519 - 1535, October 1999. https://doi.org/10.1214/aos/1017939140

Information

Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0977.62036
MathSciNet: MR2001A:62094
Digital Object Identifier: 10.1214/aos/1017939140

Subjects:
Primary: 62E25, 62F10, 62H12, 62J99
Secondary: 60F05, 62F10, 62F12, 62H25

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 5 • October 1999
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