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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 β+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 β and the function g(·) 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 β 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