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

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Functional data analysis is increasingly important.
• Characterizing associations between two-way functional predictors and scalar responses remains challenging.

Purpose of the Study:

• Propose a novel two-way functional linear model for scalar response and two-way functional predictor.
• Develop an interpretable model that captures relationships between each dimension of the predictor and the response.

Main Methods:

• Utilize product functional principal component analysis.
• Employ an iterative least squares procedure for estimating regression functions.
• Develop estimation within the framework of weak separability.

Main Results:

• The proposed method demonstrates solid performance in extensive simulation studies.
• The model effectively captures the relationship between two-way functional predictors and scalar responses.
• The approach is illustrated using a real-world mortality dataset.

Conclusions:

• The novel two-way functional linear model provides an intuitive and interpretable approach.
• The developed estimation method is robust and effective for analyzing complex functional data.
• The procedure is useful for applications in various fields, including mortality studies.