Estimation of semi-varying coefficient error-in-variable models with surrogate data and validation sample

Abstract

In this study, a semi-varying coefficient error-in-variable model with surrogate data and validation sample is proposed. Without specifying any error structure, we firstly use the local linear kernel smoothing technique to define the estimators and the proposed estimators are proved to be asymptotically normal. Then, we conduct generalized likelihood ratio (GLR) test on varying coefficient function. The data–driven bandwidth selection method is discussed. Finally, simulated studies are conducted to illustrate the finite sample properties of the proposed estimators and efficiency of the GLR methodology.

Keywords:

• GLR test
• Profile least-square method
• Semi-varying coefficient error-in-variable model
• Surrogate data
• Validation sample

Acknowledgments

The authors thank the Editor, an Associate Editor and two referees for their constructive comments, which led to significant improvements of the paper.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11471160, 11971171), the National Statistical Science Research Major Program of China (Grant No. 2018LD01), the Fundamental Research Funds for the Central Universities (Grant Nos. 30920130111015).