Journal
BIOMETRIKA
Volume 94, Issue 3, Pages 569-584Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asm038
Keywords
central subspace; Sigma-envelope; singularity of sample covariance
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Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d < n linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the ( n, p) relationship. Simulations show that our method compares favourably with standard large sample techniques when the latter are applicable. We illustrate our method with a genomics application.
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