Direction estimation in single-index models via distance covariance

We introduce a new method for estimating the direction in single-index models via distance covariance. Our method keeps model-free advantage as a dimension reduction approach. In addition, no smoothing technique is needed, which enables our method to work efficiently when many predictors are discret...

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Bibliographic Details
Published in:Journal of multivariate analysis 2013-11, Vol.122, p.148-161
Main Authors: Sheng, Wenhui, Yin, Xiangrong
Format: Article
Language:English
Subjects:
Asymptotic methods
Brownian distance covariance
Central subspace
Comparative studies
Distance covariance
Estimating techniques
Mathematical models
Single-index model
Sufficient dimension reduction
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Summary:We introduce a new method for estimating the direction in single-index models via distance covariance. Our method keeps model-free advantage as a dimension reduction approach. In addition, no smoothing technique is needed, which enables our method to work efficiently when many predictors are discrete or categorical. Under regularity conditions, we show that our estimator is root-n consistent and asymptotically normal. We compare the performance of our method with some dimension reduction methods and the single-index estimation method by simulations and show that our method is very competitive and robust across a number of models. Finally, we analyze the UCI Adult Data Set to demonstrate the efficacy of our method.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2013.07.003