Quantile regression in functional linear semiparametric model

ABSTRACT

This paper proposes nonparametric estimation methods for functional linear semiparametric quantile regression, where the conditional quantile of the scalar responses is modelled by both scalar and functional covariates and an additional unknown nonparametric function term. The slope function is estimated using the functional principal component basis and the nonparametric function is approximated by a piecewise polynomial function. The asymptotic distribution of the estimators of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. The asymptotic distribution of the estimator of the unknown nonparametric function is also established. Simulation studies are conducted to investigate the finite-sample performance of the proposed estimators. The proposed methodology is demonstrated by analysing a real data from ADHD-200 sample.

KEYWORDS:

• Functional linear semiparametric model
• quantile regression
• asymptotic distribution
• convergence rate
• ADHD

Acknowledgments

We would like to thank an Associate Editor and two anonymous referees for constructive comments that helped to improve the quality of the paper. Dr Kong wanted to thank the support of the Canadian Statistical Sciences Institute Collaborative Research Team (CANSSI-CRT), the Program on Challenges in Computational Neuroscience (CCNS) at the Statistical and Applied Mathematical Sciences Institute (SAMSI) during his visit in 2016.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Social Science Foundation of China (16BTJ019) and Jiangsu Natural Science Foundation of China (BK20151481). Research of L. Kong was supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Statistical Sciences Institute Collaborative Research Team (CANSSI-CRT). He also wanted to the support of the Program on Challenges in Computational Neuroscience (CCNS) at the Statistical and Applied Mathematical Sciences Institute (SAMSI) during his visit in 2016.