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High-dimensional Sufficient Dimension Reduction through principal projections

Author

Listed:
  • Pircalabelu, Eugen

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Artemiou, Andreas

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.

Suggested Citation

  • Pircalabelu, Eugen & Artemiou, Andreas, 2022. "High-dimensional Sufficient Dimension Reduction through principal projections," LIDAM Reprints ISBA 2022007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2022007
    Note: In: Electronic Journal of Statistics, 2022
    as

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