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Robust functional data analysis: From sparse to dense designs

Lingxuan Shao & Fang Yao

Bernoulli2026https://doi.org/10.3150/25-bej1920article
ABDC A
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0.50

Abstract

We propose a new perspective to conduct robust functional data analysis of discretely observed functional data ranging from sparse to dense sampling designs. This analysis caters to processes with various distributions, including heavy-tailed, skewed, or contaminated distributions. We study the robust functional mean (M-location) and introduce a robust dimension reduction method via principal component analysis. Theoretical outcomes for the robust functional mean and eigenfunction estimates, derived from pooled discretely observed data, are elucidated, matching their non-robust counterparts. The established convergence rates for these estimated eigenfunctions, with indices increasing with sample size, pave the way for further modeling and analysis.

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https://doi.org/https://doi.org/10.3150/25-bej1920

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@article{lingxuan2026,
  title        = {{Robust functional data analysis: From sparse to dense designs}},
  author       = {Lingxuan Shao & Fang Yao},
  journal      = {Bernoulli},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.3150/25-bej1920},
}

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