A Note on Sliced Inverse Regression with Regularizations

Authors

  • C. Bernard-Michel,

    1. Laboratoire Jean-Kuntzmann and INRIA Rhône-Alpes, team Mistis, Inovallée, 655, av. de l'Europe, Montbonnot, 38334 Saint-Ismier cedex, France
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  • L. Gardes,

    1. Laboratoire Jean-Kuntzmann and INRIA Rhône-Alpes, team Mistis, Inovallée, 655, av. de l'Europe, Montbonnot, 38334 Saint-Ismier cedex, France
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  • S. Girard

    Corresponding author
    1. Laboratoire Jean-Kuntzmann and INRIA Rhône-Alpes, team Mistis, Inovallée, 655, av. de l'Europe, Montbonnot, 38334 Saint-Ismier cedex, France
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email:Stephane.Girard@inrialpes.fr

Abstract

Summary In Li and Yin (2008, Biometrics64, 124–131), a ridge SIR estimator is introduced as the solution of a minimization problem and computed thanks to an alternating least-squares algorithm. This methodology reveals good performance in practice. In this note, we focus on the theoretical properties of the estimator. It is shown that the minimization problem is degenerated in the sense that only two situations can occur: Either the ridge SIR estimator does not exist or it is zero.

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