Statistical estimation for a partially linear single-index model with errors in all variables

This article considers partially linear single-index models with errors in all variables. By using the Pseudo - theta method (Liang, Hardle, and Carroll 1999), local linear regression and simulation-extrapolation (SIMEX) technique (Cook and Stefanski 1994), we propose an efficient methodology to estimate the current model. Under certain conditions the asymptotic properties of proposed estimators are obtained. Some simulation experiments and an application are conducted to illustrate our proposed method.