The Annals of Statistics

Structure Adaptive Approach for Dimension Reduction

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

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Abstract

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

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

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015345954

Digital Object Identifier
doi:10.1214/aos/1015345954

Mathematical Reviews number (MathSciNet)
MR1891738

Zentralblatt MATH identifier
1043.62052

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1015345954


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  • ENSAI, Campus Ker Lann rue B.Pascal 35170 Bruz France E-mail: hristach@ensai.fr A.Juditsky LMC Domaine Universitaire B.P.53 38041 Grenoble Cedex 9 France E-mail: anatoli.iouditski@inrialpes.fr