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Annual Review of Statistics and Its Application

Volume 12, 2025

Empirical Likelihood in Functional Data Analysis

  • Hsin-wen Chang1 and Ian W. McKeague2
  • 1Institute of Statistical Science, Academia Sinica, Taipei, Taiwan; email: [email protected] 2Department of Biostatistics, Columbia University, New York, NY, USA
  • Vol. 12:425-448 (Volume publication date March 2025)
  • First published as a Review in Advance on November 12, 2024
  • Copyright © 2025 by the author(s).
    This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information.

Abstract

Functional data analysis (FDA) studies data that include infinite-dimensional functions or objects, generalizing traditional univariate or multivariate observations from each study unit. Among inferential approaches without parametric assumptions, empirical likelihood (EL) offers a principled method in that it extends the framework of parametric likelihood ratio–based inference via the nonparametric likelihood. There has been increasing use of EL in FDA due to its many favorable properties, including self-normalization and the data-driven shape of confidence regions. This article presents a review of EL approaches in FDA, starting with finite-dimensional features, then covering infinite-dimensional features. We contrast smooth and nonsmooth frameworks in FDA and show how EL has been incorporated into both of them. The article concludes with a discussion of some future research directions, including the possibility of applying EL to conformal inference.

Keyword(s): dynamic correlation, functional ANOVA, functional linear models, pointwise and simultaneous inference
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2025-03-07
2025-06-15
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Empirical Likelihood in Functional Data Analysis
Annual Review of Statistics and Its Application 12, 425 (2025); https://doi.org/10.1146/annurev-statistics-112723-034225
/content/journals/10.1146/annurev-statistics-112723-034225
/content/journals/10.1146/annurev-statistics-112723-034225
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