A New Algorithm for Estimating the Effective Dimension-Reduction Subspace

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. Many methods for estimating the EDR subspace perform principal component analysis on a family of vectors, say ^1,..., ^L, nearly lying in the EDR subspace. This is in particular the case for the structure-adaptive approach proposed by Hristache et al. (2001a). In the present work, we propose to estimate the projector onto the EDR subspace by the solution to the optimization problem minimize max =1,...,L ^ (I -A)^ subject to A Am , where Am is the set of all symmetric matrices with eigenvalues in [0,1] and trace less than or equal to m, with m being the true structural dimension. Under mild assumptions, n-consistency of the proposed procedure is proved (up to a logarithmic factor) in the case when the structural dimension is n...

• Type: Journal
• Year: 2008
• Where: JMLR
• Authors: Arnak S. Dalalyan, Anatoly Juditsky, Vladimir Spokoiny
• Keywords: EDR Subspace, Estimating, JMLR 2008, Multi-index Regression Model