Uncertainty Estimation in Functional Linear Models

TL;DR

This paper develops a new method for estimating uncertainty in functional linear mixed models, providing theoretically valid approximations and demonstrating improved performance over existing techniques in numerical examples.

Contribution

It introduces a novel approach for uncertainty estimation in functional linear mixed models with finite curves, including approximation techniques and modified estimation methods.

Findings

The proposed method provides valid uncertainty measurements.

It is computationally simple and outperforms existing methods.

Numerical examples demonstrate effectiveness and accuracy.

Abstract

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense. The recent literature develops several techniques for registering the curves and associated model estimation. However, very little has been investigated for statistical inference, specifically uncertainty estimation. In this article, we consider functional linear mixed modeling approach to combine several curves. We concentrate measuring uncertainty when the functional linear mixed models are used for prediction. Although measuring the uncertainty is paramount interest in any statistical prediction, there is no closed form expression available for functional mixed effects models. In many real life applications only a finite number of curves can be observed. In such situations it is important to asses the error rate for any valid statistical statement. We derive theoretically valid approximation of uncertainty measurements that are suitable along with modified estimation techniques. We illustrate our methods by numerical examples and compared with other existing literature as appropriate. Our method is computationally simple and often outperforms the other methods.