https://github.com/computorg/published-202606-devijver-scb

Repo for the Computo paper entitled Should we correct the bias in Confidence Bands for Repeated Functional Data?
https://github.com/computorg/published-202606-devijver-scb

bias confidence-band dimension-selection functional-data kac-rice repeated-data

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Repo for the Computo paper entitled Should we correct the bias in Confidence Bands for Repeated Functional Data?

• Host: GitHub
• URL: https://github.com/computorg/published-202606-devijver-scb
• Owner: computorg
• Created: 2024-05-30T10:23:55.000Z (about 2 years ago)
• Default Branch: main
• Last Pushed: 2026-06-30T15:49:43.000Z (8 days ago)
• Last Synced: 2026-06-30T17:25:06.910Z (8 days ago)
• Topics: bias, confidence-band, dimension-selection, functional-data, kac-rice, repeated-data
• Language: TeX
• Homepage: https://computo-journal.org/published-202606-devijver-scb/
• Size: 10.3 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 3
• Metadata Files:
  • Readme: README.md

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README

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

Emilie Devijver, Adeline Samson

2026-06-30

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[![DOI:10.57750/nmyg-wg36](https://img.shields.io/badge/DOI-10.57750/nmyg--wg36-034E79.svg)](https://doi.org/10.57750/nmyg-wg36)

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### Authors

- [Emilie Devijver](https://lig-aptikal.imag.fr/~devijvee/) (CNRS, Univ.

  Grenoble Alpes, Grenoble INP, LIG, 38000 Grenoble, France)

- [Adeline Samson](http://adeline.e-samson.org) (Univ. Grenoble Alpes,

  CNRS, Grenoble INP, LJK, 38000 Grenoble, France)

### Abstract

While confidence intervals for finite quantities are well-established,

constructing confidence bands for objects of infinite dimension, such as

functions, is challenging. In this paper, we explore 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

into the confidence bands when the dimension of the basis is

misspecified. Building on this insight, we introduce a corrected,

unbiased confidence band. Surprisingly, our corrected band tends to be

wider than that suggested by a naive approach. 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

through an extensive simulation study. We conclude with an application

to real data.