The Annals of Statistics

Structure Adaptive Approach for Dimension Reduction

Marian Hristache, Anatoli Juditsky, Jörg Polzehl, and Vladimir Spokoiny

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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.

Article information

Ann. Statist., Volume 29, Number 6 (2001), 1537-1566.

First available in Project Euclid: 5 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62H40 62G20: Asymptotic properties

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


Hristache, Marian; Juditsky, Anatoli; Polzehl, Jörg; Spokoiny, Vladimir. Structure Adaptive Approach for Dimension Reduction. Ann. Statist. 29 (2001), no. 6, 1537--1566. doi:10.1214/aos/1015345954.

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