A0789
Title: Should we correct the bias in confidence bands for repeated functional data?
Authors: Emilie Devijver - CNRS (France) [presenting]
Adeline Leclercq-Samson - LJK universite Joseph Fourier (France)
Abstract: While confidence intervals for finite quantities are well-established, constructing confidence bands for objects of infinite dimension, such as functions, poses challenges. The concept of parametric confidence bands is explored for functional data with an orthonormal basis. Specifically, the method proposed by a prior study is revisited, 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, a corrected, unbiased confidence band is introduced. Surprisingly, the corrected band tends to be wider than what a naive approach would suggest. To address this, a model selection criterion that allows for data-driven estimation of the basis dimension is proposed. The bias is then automatically corrected after dimension selection. These strategies are illustrated using an extensive simulation study. It is concluded with an application to real data.
