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Adaptive variable selection in nonparametric sparse regression
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 214-244 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the problem of exact recovery of an unknown multivariate function $f$ observed in the continuous regression model. It is assumed that, in addition to some smoothness constraints, $f$ possesses an additive sparse structure determined by the sparsity index $\beta\in (0,1)$. As a consequence of the additive sparsity assumption, the recovery problem transforms to a variable selection problem. Conditions for exact variable selection are provided, and a family of asymptotically minimax variable selection procedures is constructed. The procedures are adaptive in the sparsity index $\beta$. 
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Yu. I. Ingster; N. A. Stepanova. Adaptive variable selection in nonparametric sparse regression. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 214-244. http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a13/

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