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Estimation in a semiparametric partially linear errors-in-variables model. (English) Zbl 0977.62036
Summary: We consider the partially linear model relating a response $Y$ to predictors $(X,T)$ with mean function $X^T\beta +g(T)$ when the $X$’s are measured with additive error. The semiparametric likelihood estimate of {\it T.A. Severini} and {\it J.G. Staniswalis} [J. Am. Stat. Assoc. 89, No. 426, 501-511 (1994; Zbl 0798.62046)] 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 whieh 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.

62G05Nonparametric estimation
62E20Asymptotic distribution theory in statistics
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
Full Text: DOI
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[14] COLLEGE STATION, TEXAS 77843-3143 E-MAIL: carroll@stat.tamu.edu