A new algorithm for estimating the effective dimension-reduction subspace

Arnak S. Dalalyan (1) , Anatoli B. Juditsky (2) , Vladimir Spokoiny (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 SMS - Statistique et Modélisation Stochatisque
3 Weierstrass-Institute

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.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

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