Estimation for semi-functional linear regression

Abstract

This paper studies estimation in semi-functional linear regression. A general formulation is used to treat mean regression, median regression, quantile regression and robust mean regression in one setting. The linear slope function is estimated by the functional principal component basis and the nonparametric component is approximated by a B-spline function. The global convergence rates of the estimators of unknown slope function and nonparametric component are established under suitable norm. The convergence rate of the mean-squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.

Keywords:

• semi-functional linear regression
• quantile estimator
• functional principal component analysis
• convergence rate

Acknowledgements

The author thank anonymous referees for their valuable comments and suggestions, which improved substantially the early version of this paper.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11071120] and the Humanities and Social Science Foundation of Ministry of Education of China [grant number 14YJA910004].