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Gradient‐based approach to sufficient dimension reduction with functional or longitudinal covariates

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  • Ming‐Yueh Huang
  • Kwun Chuen Gary Chan

Abstract

In this paper, we focus on the sufficient dimension reduction problem in regression analysis with real‐valued response and functional or longitudinal covariates. We propose a new method based on gradients of the conditional distribution function to estimate the sufficient dimension reduction subspace. While existing inverse‐regression‐type methods relies on a linearity condition, our method is based on the gradient of conditional distribution function and its validity only requires smoothness conditions on the population parameters. Practically, the proposed estimator can be obtained by standard algorithm of functional principal component analysis. The proposed method is demonstrated through extensive simulations and two empirical examples.

Suggested Citation

  • Ming‐Yueh Huang & Kwun Chuen Gary Chan, 2024. "Gradient‐based approach to sufficient dimension reduction with functional or longitudinal covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1567-1586, December.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:4:p:1567-1586
    DOI: 10.1111/sjos.12724
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    References listed on IDEAS

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