Variable selection in high-dimensional additive models based on norms of projections

2014/05/31 by Martin Wahl, Wahl, Martin · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Statistical Methods and Inference #math.ST #msc:62G05 #msc:62G08 #msc:94A12 #stat.TH

paper · pdf · doi:10.48550/arxiv.1406.0052

27 pages

arxiv created 2015/02/01 · arxiv updated 2015/02/03

Abstract

We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in Hilbert spaces and consists of comparing the norms of the projections of the data onto various additive subspaces. Under minimal geometric assumptions, we prove concentration inequalities which lead to new conditions under which consistent variable selection is possible. As an application, we establish conditions under which a single component can be estimated with the rate of convergence corresponding to the situation in which the other components are known.

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