High-dimensional sufficient dimension reduction through principal projections

Pircalabelu, Eugen and Artemiou, Andreas ORCID: https://orcid.org/0000-0002-7501-4090 2022. High-dimensional sufficient dimension reduction through principal projections. Electronic Journal of Statistics 16 (1) , pp. 1804-1830. 10.1214/22-EJS1988

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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 non-invertibility 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Rights: Creative Commons Attribution 4.0 International License
Publisher:	Institute of Mathematical Statistics
ISSN:	1935-7524
Date of First Compliant Deposit:	28 February 2022
Date of Acceptance:	12 February 2022
Last Modified:	01 Aug 2024 10:08
URI:	https://orca.cardiff.ac.uk/id/eprint/147424

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