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Abstract:
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We consider nonparametric estimation of a regression function in an errors-in-variables (EIV) problem. In the classical EIV problem, the goal is to estimate a function m, where Y=m(V)+\epsilon and a sample of (U,Y) is available, where U=V+\delta. See Fan and Truong (1993). In this talk, we assume that a sample of (W,Y) is observed, where Y=g(W)+\varepsilon, but instead of estimating g, the goal is to estimate m(x)=E(Y|X=x), where X=W+\delta and \delta is a measurement error. The motivating idea is that a training sample of accurate observations is often available, and future values of Y can be predicted from easier-to-obtain contaminated observations X of W. We propose a nonparametric estimator of m, discuss its theoretical properties and illustrate its performance via a simulation study and on a real data example. This is joint work with Peter Hall and Hans Muller.
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