The Annals of Statistics
- Ann. Statist.
- Volume 29, Number 6 (2001), 1537-1566.
Structure Adaptive Approach for Dimension Reduction
Marian Hristache, Anatoli Juditsky, Jörg Polzehl, and Vladimir Spokoiny
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