Variable selection for partially time-varying coefficient error-in-variables models

Abstract

Partially time-varying coefficient models are useful for studying the time dependent effect of variables. In this paper, we consider the variable selection for this kind of models when covariates in parametric part are observed with additive measurement errors and the sequence of observations $\{Z_i,X_i,{\epsilon }_i\}$ is stationary and α-mixing. To select significant variables and enhance model predictability, a variable selection procedure with smoothly clipped absolute deviation (SCAD) penalty is developed via using profile least squares (PLS) method and local linear technique. Under some proper conditions, the oracle properties of the resulting estimator are established. Furthermore, we consider a test statistic based on penalized PLS method and prove theoretically that its limit is a weighted sum of standard chi-square random variables. Numerical examples are carried out to illustrate the finite sample performance of proposed approaches.

Keywords:

• time-varying coefficient models
• additive measurement errors
• profile least squaresmethod
• variable selection
• oracle properties

Acknowledgements

We are grateful to the reviewers and the editor for their helpful comments which lead to a great improvement on the quality of the previous manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Xia's work is partially supported by the Natural Science Foundation of China [grant number 11471058] and the Science and Technology Development Fund of Macau [grant number FDCT078/2012/A3]. Yang's work is supported by the National Natural Science Foundation of China [grant number 11171361].