Statistical estimation for partially linear error-in-variable models with error-prone covariates

ABSTRACT

Motivated by a heart disease data, we propose a new partially linear error-in-variable models with error-prone covariates, in which mismeasured covariate appears in the noparametric part and the covariates in the parametric part are not observed, but ancillary variables are available. In this case, we first calibrate the linear covariates, and then use the least-square method and the local linear method to estimate parametric and nonparametric components. Also, under certain conditions the asymptotic distributions of proposed estimates are obtained. Simulated and real examples are conducted to illustrate our proposed methodology.

KEYWORDS:

• Ancillary variables
• Asymptotic distributions
• Error-prone covariates
• Local linear method
• Partially linear error-in-variable model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62E20

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11471160, 11101114), the National Statistical Science Research Key Program of China (Grant No. 2013LZ45), the Fundamental Research Funds for the Central Universities (Grant No. 30920130111015) and the Jiangsu Provincial Basic Research Program (Natural Science Foundation) (Grant No. BK20131345) and sponsored by Qing Lan Project.