Sufficient Dimension Reduction via Distance Covariance

We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advanta...

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Bibliographic Details
Published in:Journal of computational and graphical statistics 2016-01, Vol.25 (1), p.91-104
Main Authors: Sheng, Wenhui, Yin, Xiangrong
Format: Article
Language:English
Subjects:
Brownian distance covariance
Central subspace
Distance covariance
Machine Learning
Mathematical models
Mathematical problems
Random variables
Simulation
Studies
Sufficient dimension reduction
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Summary:We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established for our estimator. We compare the performance of our method with some existing dimension-reduction methods by simulations and find that our method is very competitive and robust across a number of models. We also analyze the Auto MPG data to demonstrate the efficacy of our method. Supplemental materials for this article are available online.
ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2015.1026601