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

ABSTRACT

This article considers partially linear single-index models with errors in all variables. By using the Pseudo − θ method (Liang, Härdle, 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.

Keywords:

• Measurement errors
• Partially linear single-index model
• Pseudo − θ method
• SIMEX

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62E20

Acknowledgments

The authors would like to thank the referees for their valuable comments that led to a greatly improved presentation of the paper.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11471160, 11101114), the Fundamental Research Funds for the Central Universities (Grant No. 30920130111015), the Jiangsu Provincial Basic Research Program (Natural Science Foundation) (Grant No. BK20131345) and sponsored by Qing Lan Project.