Efficient semiparametric regression for longitudinal data with regularised estimation of error covariance function

ABSTRACT

Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularisation method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed-effects model. Our method utilises the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches in simulation studies. This procedure is easy to implement and its numerical performance is investigated using both simulated and real data.

KEYWORDS:

• Covariance function
• local linear regression
• method of regularisation
• profile weighted least squares
• semiparametric varying-coefficient partially linear model
• Sobolov space
• tensor product space

Acknowledgements

The authors thank the two referees for insightful comments and suggestions, and Yongsu Lee for the helps in R programming techniques.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

C. Zhang's research is supported by the U.S. NSF Division of Mathematical Sciences [grant number DMS– 1712418], Wisconsin Alumni Research Foundation, and National Natural Science Foundation of China [grant number 11690014]. Hulin Wu's reserach is supported by grants NIAID [grant number RO1 AI087135], and CPRIT [grant number RP170668].