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A new algorithm for estimating the effective dimension-reduction subspace

Arnak Dalalyan·Anatoly Juditsky·Vladimir Spokoiny
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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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Arnak Dalalyan, Anatoly Juditsky, Vladimir Spokoiny. 2007-01-30. A new algorithm for estimating the effective dimension-reduction subspace. https://arxiv.org/abs/math/0701887

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