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.
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).