Abstract
In this article, we propose an alternating inverse regression (AIR) to estimate the central subspace (CS) in a successive manner. Taking advantage of both sliced inverse regression (SIR) and partial least squares (PLS), AIR circumvents the collinearity and curse of dimensionality simultaneously. A modified BIC criterion with a penalty term achieving an optimal convergence rate is suggested to estimate the dimension of the CS. We also extend AIR to the multivariate responses case. Through illustrative examples and a real dataset, we demonstrate the usefulness of AIR, and its advantages over some existing methods. Supplemental materials for this article are available online.
Original language | English |
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Pages (from-to) | 887-899 |
Number of pages | 13 |
Journal | Journal of Computational and Graphical Statistics |
Volume | 19 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2010 |
Scopus Subject Areas
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Statistics, Probability and Uncertainty
User-Defined Keywords
- Central subspace
- Dimension reduction subspace
- Partial least squares
- Sliced inverse regression