On Partially Linear Single-Index Models with Missing Response and Error-in-Variable Predictors

Abstract

In this paper, we consider a partially linear single-index model when missing responses and nonlinear regressors with measurement error are taken into account. Utilizing data imputation for missing values and regression calibration for error-prone regressors, we not only estimate the parameters in the linear part as well as the single-index part, but also estimate the nonparametric link function by local linear fit. Under normalization, all the proposed estimators for the regression coefficients and the link function are proven to be asymptotically normal, and some illustrative simulations are provided to justify our methods.