A Note on Sliced Inverse Regression with Regularizations
Statistics Theory
2011-04-04 v1 Statistics Theory
Abstract
In "Li, L. and Yin, X. (2008). Sliced Inverse Regression with Regularizations. Biometrics, 64(1):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. Is it 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.
Keywords
Cite
@article{arxiv.1104.0098,
title = {A Note on Sliced Inverse Regression with Regularizations},
author = {Caroline Bernard-Michel and Laurent Gardes and Stéphane Girard},
journal= {arXiv preprint arXiv:1104.0098},
year = {2011}
}