Sufficient dimension reduction based on an ensemble of minimum average variance estimators

Details Sufficient dimension reduction based on an ensemble of minimum average variance estimators Sufficient dimension reduction based on an ensemble of minimum average variance estimators

2012-03-15

arxiv.org/abs/1203.3313v1

Annals of Statistics 2011, Vol. 39, No. 6, 3392-3416

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS950 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS950

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box--Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form. We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.

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