Robust functional regression model for marginal mean and subject-specific inferences

TL;DR

This paper proposes robust functional regression models utilizing heavy-tailed processes like Student t-processes, offering reliable inference and prediction in the presence of data contamination or distribution misspecification.

Contribution

It introduces flexible robust models with efficient algorithms for marginal and subject-specific inferences, including bootstrap prediction intervals, enhancing robustness in functional data analysis.

Findings

Models are robust against data contamination.

Prediction intervals maintain nominal confidence levels.

Numerical studies validate the effectiveness of the proposed methods.

Abstract

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals for conditional mean curves. Numerical studies show that the proposed model provides robust analysis against data contamination or distribution misspecification, and the proposed prediction intervals maintain the nominal confidence levels. A real data application is presented as an illustrative example.