High-dimensional Sufficient Dimension Reduction through principal projections

Eugen Pircalabelu and Andreas Artemiou
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Eugen Pircalabelu: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022007, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We develop in this work a new dimension reduction method for high-dimensional settings. The proposed procedure is based on a principal support vector machine framework where principal projections are used in order to overcome the noninvertibility of the covariance matrix. Using a series of equivalences we show that one can accurately recover the central subspace using a projection on a lower dimensional subspace and then applying an ℓ1 penalization strategy to obtain sparse estimators of the sufficient directions. Based next on a desparsified estimator, we provide an inferential procedure for high-dimensional models that allows testing for the importance of variables in determining the sufficient direction. Theoretical properties of the methodology are illustrated and computational advantages are demonstrated with simulated and real data experiments.

Keywords: Sufficient dimension reduction; Support vector machines; Quadratic programming; ℓ1 penalized estimation; Debiased estimator (search for similar items in EconPapers)
Pages: 30
Date: 2022-02-01
Note: In: Electronic Journal of Statistics, 2022
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2022007

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