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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 T.A. Severini and 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.

MSC:
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
Software:
XploRe
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References:
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[14] COLLEGE STATION, TEXAS 77843-3143 E-MAIL: carroll@stat.tamu.edu
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