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December 2001 Structure Adaptive Approach for Dimension Reduction
Marian Hristache, Anatoli Juditsky, Jörg Polzehl, Vladimir Spokoiny
Ann. Statist. 29(6): 1537-1566 (December 2001). DOI: 10.1214/aos/1015345954


We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension $m$ of the index space does not exceed 3, this space can be estimated with the rate $n^{-1/2}$ under rather mild assumptions on the model.


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Marian Hristache. Anatoli Juditsky. Jörg Polzehl. Vladimir Spokoiny. "Structure Adaptive Approach for Dimension Reduction." Ann. Statist. 29 (6) 1537 - 1566, December 2001.


Published: December 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1043.62052
MathSciNet: MR1891738
Digital Object Identifier: 10.1214/aos/1015345954

Primary: 62G05
Secondary: 62G20 , 62H40

Keywords: average derivative estimation , Dimensioin-reduction , index space , multi-index model , structural adaptation

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 6 • December 2001
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