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Abstract:
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Sufficient dimension reduction, replacing the original predictors with a few linear combinations while keeping all the regression information, has been widely used in the past thirty years or so. In this paper, we propose a new sufficient dimension reduction method, with two estimation procedures, for estimating central mean subspace through a novel approach of feature fi lter. Our method is suitable for both univariate and multivariate responses. Asymptotic results are established. Furthermore, we provide estimation methods to determine the structural dimension, to obtain a sparse estimator and to deal with large p small n data. The efficacy of our method is demonstrated by simulations and a real data example.
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