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Biometrika 2005 92(2):371-384; doi:10.1093/biomet/92.2.371
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© 2005 Biometrika Trust

Direction estimation in single-index regressions

Xiangrong Yin1 and R. Dennis Cook2

1 Department of Statistics, 204 Statistics Building, University of Georgia, Athens, Georgia 30602, U.S.A. xryin{at}stat.uga.edu, 2 School of Statistics, 1994 Buford Avenue, University of Minnesota, St. Paul, Minnesota 55108, U.S.A. dennis{at}stat.umn.edu

We propose a general dimension-reduction method that combines the ideas of likelihood, correlation, inverse regression and information theory. We do not require that the dependence be confined to particular conditional moments, nor do we place restrictions on the predictors or on the regression that are necessary for methods like ordinary least squares and sliced-inverse regression. Although we focus on single-index regressions, the underlying idea is applicable more generally. Illustrative examples are presented.

Key Words: Central mean subspace; Central subspace; Dimension-reduction subspace; Regression graphics; Single-index model

Received May 2003. Revised August 2004.


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