Abstract
Modern graphical tools have enhanced our ability to learn many things from data directly. In recent years, dimension reduction has proven to be an effective tool for generating low-dimensional summary plots without appreciable loss of information. Some well-known inverse regression methods for dimension reduction such as sliced inverse regression (Li, 1991) and sliced average variance estimation (Cook & Weisberg, 1991) have been developed to estimate summary plots for regression and discriminant analysis. In this paper, we suggest a new method that makes use of inverse third moments. This method can find structure beyond that found by sliced inverse regression and sliced average variance estimation, particularly regression mixtures. Illustrative examples are presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 113-125 |
| Number of pages | 13 |
| Journal | Biometrika |
| Volume | 90 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2003 |
Bibliographical note
Funding Information:The authors would like to thank the editor, the associate editor and referees whose suggestions led to a greatly improved paper. The work of Yin was supported in part by the University of Georgia Research Foundation and the work of Cook was supported in part by grants from the U.S. National Science Foundation.
Keywords
- Central subspace
- Dimension-reduction subspace
- Inverse regression method
- Regression graphics