Additive Partial Linear Models with Measurement Errors.

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and SIMEX estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require undersmoothing of the nonparametric component in order for the estimator of the parametric component be root-n consistent. This feature stems from a decrease of the bias of the resulting estimator which is appropriately derived using a profile procedure. A similar characteristic in semiparametric partially linear models was obtained by Wang et al. (2005). We also discuss the asymptotics of the proposed SIMEX approach. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to a dataset from a semen study.