Should we correct the bias in Confidence Bands for Repeated Functional Data?

Emilie Devijver, Adeline Samson

Abstract:

While confidence intervals for finite quantities are well-established, constructing confidence bands for objects of infinite dimension, such as functions, poses challenges. In this paper, weexplore the concept of parametric confidence bands for functional data with an orthonormal basis. Specifically, we revisit the method proposed by Sun and Loader, which yields confidence bands for the projection of the regression function in a fixed-dimensional space. This approach can introduce bias in the confidence bands when the dimension of the basis is misspecified.Leveraging this insight, we introduce a corrected, unbiased confidence band. Surprisingly, our corrected band tends to be wider than what a naive approach would suggest. To address this, we propose a model selection criterion that allows for data-driven estimation of the basis dimension.The bias is then automatically corrected after dimension selection. We illustrate these strategies using an extensive simulation study. We conclude with an application to real data.

gh-page: https://emiliedevijver.github.io/SCB/

Repository Url: https://github.com/EmilieDevijver/SCB

Changes Since Last Submission: We have updated the theoretical results, rewritten the introduction to motivate our work with respect to the literature, add competitive methods in the experimental sections.

Assigned Action Editor: ~Pierre_Neuvial1

Submission Number: 27