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February 2014 On efficient dimension reduction with respect to a statistical functional of interest
Wei Luo, Bing Li, Xiangrong Yin
Ann. Statist. 42(1): 382-412 (February 2014). DOI: 10.1214/13-AOS1195


We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the linear functional, the composite linear functional and the implicit functional. In conjunction with our theoretical analysis, we also propose a class of one-step Newton–Raphson estimators and show by simulations that they substantially outperform existing methods. Finally, we apply the new method to construct the central mean and central variance subspaces for a data set involving the physical measurements and age of abalones, which exhibits a strong pattern of heteroscedasticity.


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Wei Luo. Bing Li. Xiangrong Yin. "On efficient dimension reduction with respect to a statistical functional of interest." Ann. Statist. 42 (1) 382 - 412, February 2014.


Published: February 2014
First available in Project Euclid: 19 March 2014

zbMATH: 1285.62072
MathSciNet: MR3189490
Digital Object Identifier: 10.1214/13-AOS1195

Primary: 62-09 , 62G99 , 62H99

Keywords: central subspace , conditional mean , efficient information , efficient score , Fréchet derivative and its representation , projection , tangent space , variance and quantile

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 1 • February 2014
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