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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
XploRe
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##### References:
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