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We study a broad family of lower-rank spline estimators for the mean of a process X based on discretely sampled functional data observed with measurement error. We derive its rates of convergence under general assumptions and show that the parametric rate n−1 is attainable, even under discretely sampled data with heavytailed distributions of either the functional variable or the measurement error.

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Robust Penalized Splines for Location Estimation from Discretely Sampled Functional Data

  • 会议论文

  • 发表日期：

    2025年

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  • Ioannis Kalogridis,
  • Stefan Van Aelst

摘要

We study a broad family of lower-rank spline estimators for the mean of a process X based on discretely sampled functional data observed with measurement error. We derive its rates of convergence under general assumptions and show that the parametric rate n−1 is attainable, even under discretely sampled data with heavytailed distributions of either the functional variable or the measurement error.