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<p>We introduce a novel approach for modeling two-way functional trajectories, relying on Kendall’s tau representation of marginal covariance functions and utilizing the concept of product functional principal component analysis. The developed estimation procedure is intuitive and straightforward to implement. Theoretical results supporting its validity are also established. Numerical simulation studies validate its superior performance compared to recently developed methods. Furthermore, the application of this approach to analyze two-way air pollution trajectories demonstrates its practical superiority.</p>

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Robust Product Functional Principal Component Analysis

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Xingyu Yan,
  • Peng Zhao,
  • Jiaqian Yu,
  • Pengcheng Ren,
  • Weiyong Ding

摘要

We introduce a novel approach for modeling two-way functional trajectories, relying on Kendall’s tau representation of marginal covariance functions and utilizing the concept of product functional principal component analysis. The developed estimation procedure is intuitive and straightforward to implement. Theoretical results supporting its validity are also established. Numerical simulation studies validate its superior performance compared to recently developed methods. Furthermore, the application of this approach to analyze two-way air pollution trajectories demonstrates its practical superiority.