A novel two-way functional linear model with applications in human mortality data analysis

Abstract

Recently, two-way or longitudinal functional data analysis has attracted much attention in many fields. However, little is known on how to appropriately characterize the association between two-way functional predictor and scalar response. Motivated by a mortality study, in this paper, we propose a novel two-way functional linear model, where the response is a scalar and functional predictor is two-way trajectory. The model is intuitive, interpretable and naturally captures relationship between each way of two-way functional predictor and scalar-type response. Further, we develop a new estimation method to estimate the regression functions in the framework of weak separability. The main technical tools for the construction of the regression functions are product functional principal component analysis and iterative least square procedure. The solid performance of our method is demonstrated in extensive simulation studies. We also analyze the mortality dataset to illustrate the usefulness of the proposed procedure.

Keywords:

• Functional data
• two-way functional data
• two-way functional linear regression
• product functional principal components analysis
• weak separability
• matrix variate

Mathematic Subject classification:

• 62-08

Acknowledgments

The authors sincerely acknowledge the efforts of the Editor, the Associate Editor and two anonymous referees that have resulted in significant improvements of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 12101270, 12325109, 12301597], The Humanities and Social Sciences Project of the Ministry of Education [grant numbers 21YJC910001], and the Graduate Research and Innovation Program in Jiangsu Province [grant numbers KYCX22 2834].