Partially linear single-index measurement error models

We consider a partially linear single-index model Y = eta (Z(T) alpha(0))+X-T beta(0+epsilon) when X is measured with additive error. Estimators in the literature are biased when the measurement errors are ignored. We propose two estimators in this setting and develop their asymptotic normality. We apply the proposed estimators to the analysis of dietary data, and provide the results of a simulation experiment to illustrate our approach.