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A new algorithm for estimating the effective dimension-reduction subspace

Abstract : The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is proposed. Under mild assumptions, $\sqrt n$-consistency of the proposed procedure is proved (up to a logarithmic factor) in the case when the structural dimension is not larger than $4$. The empirical behavior of the algorithm is studied through numerical simulations.
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https://hal.archives-ouvertes.fr/hal-00128129
Contributor : Arnak Dalalyan <>
Submitted on : Wednesday, April 18, 2007 - 10:31:09 PM
Last modification on : Tuesday, December 8, 2020 - 3:40:26 AM
Long-term archiving on: : Monday, June 27, 2011 - 3:42:26 PM

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Arnak S. Dalalyan, Anatoly Juditsky, Vladimir Spokoiny. A new algorithm for estimating the effective dimension-reduction subspace. Journal of Machine Learning Research, Microtome Publishing, 2008, 9, pp.1647-1678. ⟨hal-00128129v2⟩

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