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Biometrika 2006 93(1):65-74; doi:10.1093/biomet/93.1.65
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© 2006 Biometrika Trust

Using intraslice covariances for improved estimation of the central subspace in regression

R. Dennis Cook1 and Liqiang Ni2

1 School of Statistics, University of Minnesota, St. Paul, Minnesota 55108, U.S.A. dennis{at}stat.umn.edu, 2 Department of Statistics and Actuarial Science, University of Central Florida, Orlando, Florida 32816, U.S.A. lni{at}mail.ucf.edu

Popular methods for estimating the central subspace in regression require slicing a continuous response. However, slicing can result in loss of information and in some cases that loss can be substantial. We use intraslice covariances to construct improved inference methods for the central subspace. These methods are optimal within a class of quadratic inference functions and permit chi-squared tests of conditional independence hypotheses involving the predictors. Our experience gained through simulation is that the new method is never worse than existing methods, and can be substantially better.

Key Words: Inverse regression estimation; Sliced inverse regression; Sufficient dimension reduction

Received October 2004. Revised August 2005.


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