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

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 subspac...

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Veröffentlicht in:Scandinavian journal of statistics 2024-12, Vol.51 (4), p.1567-1586
Hauptverfasser: Huang, Ming‐Yueh, Chan, Kwun Chuen Gary
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12724