Model estimation and selection for partial linear varying coefficient EV models with longitudinal data

Abstract

In this paper, we consider the estimation and model selection for longitudinal partial linear varying coefficient errors-in-variables (EV) models when the covariates are measured with some additive errors. Bias-corrected penalized quadratic inference functions method is proposed based on quadratic inference functions with two penalty function terms. The proposed method can not only handle the measurement errors of covariates and within-subject correlations but also estimate and select significant non-zero parametric and nonparametric components simultaneously. With some regularization conditions, the resulting estimators of parameters are asymptotically normal and the estimators of nonparametric varying coefficient achieves the optimal convergence rate. Furthermore, we present simulation studies and a real example analysis to evaluate the finite sample performance of the proposed method.

Keywords:

• Longitudinal data
• variable selection
• partial linear varying coefficient EV models
• quadratic inference function

Acknowledgements

This work is supported by grants from the Social Science Foundation of China (15CTJ008 to MZ), the Natural Science Foundation of Anhui Universities (KJ2017A433 to KZ), the Social Science Foundation of the Ministry of Education of China(19YJCZH250 to KZ), the National Science Foundation of China (12071305, 11871390 and 11871411 to YZ), the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province(gxyqZD2019031 to YZ), the National Science Foundation of China (71803001 to YZ). This paper is partially supported by the National Natural Science Foundation of China (11901401). All authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by grants from the Social Science Foundation of China [grant number 15CTJ008 to M. Z.], the Natural Science Foundation of Anhui Universities [grant number KJ2017A433 to K. Z.], the Social Science Foundation of the Ministry of Education of China [grant number 19YJCZH250 to K. Z.], the National Science Foundation of China [grant numbers 12071305, 11871390 and 11871411 to Y. Z.], the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province [grant number gxyqZD2019031 to Y. Z.], the National Science Foundation of China [grant number 71803001 to Y. Z.]. This paper is partially supported by the National Natural Science Foundation of China [grant number 11901401].