Statistica Sinica 15(2005), 99-116

PARTIALLY LINEAR SINGLE-INDEX MEASUREMENT

ERROR MODELS

Hua Liang and Naisyin Wang

St. Jude Children's Research Hospital and Texas A &M University

Abstract: We consider a partially linear single-index model $Y=\eta(Z^{{\mbox{\rm\scriptsize T} }}\alpha_0)+X^{{\mbox{\rm\scriptsize T} }}\beta_0+\varepsilon$ 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.

Key words and phrases: Local linear regression, nonparametric regression, semiparametric estimation.