A New Functional Estimation Procedure for Varying Coefficient Models

Abstract

There has been substantial research interest in developing various estimation procedures for varying coefficient models. Most methods in the literature require specifying a working covariance structure. In case of a misspecified structure, estimation of the varying coefficient function may be deficient. Taking advantage of functional principal component analysis, we propose a new functional estimation procedure for varying coefficient models which does not need a working covariance structure. Weak convergence property for the proposed estimators has been established. Based on the simulation studies, the proposed procedure works better than the naive local linear regression with working independence error structure by Zhu et al. and Cholesky decomposition method by Lin et al. We apply our method to analyze the growth data of newborn infants in a real medical study and produce interpretable results.

Keywords:

• Varying coefficient models
• within-subject correlation
• functional principal component analysis
• local linear regression

Acknowledgements

We are grateful to anonymous reviewers for detailed and constructive comments, which led to many improvements. Our special thanks go to Dr. Hongmei Lin (Shanghai University of International Business and Economics) for sharing codes.

Additional information

Funding

The work was supported by National Natural Science Foundation of China (project number: 11771146), the 111 Project (B14019) and Program of Shanghai Subject Chief Scientist (14XD1401600). The work was also supported by grants from the National Natural Science Foundation of China (11771145) and (11801210) and the China Postdoctoral Science Foundation (2018M630393).