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 sparsity index β ∈ (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 with respect to the sparsity index β. Bibliography: 18 titles.

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Persistent URL dx.doi.org/10.1007/s10958-014-1846-7
Journal Journal of Mathematical Sciences (United States)
Ingster, Y. (Yu.), & Stepanova, N. (2014). Adaptive Variable Selection in Nonparametric Sparse Regression. Journal of Mathematical Sciences (United States), 199(2), 184–201. doi:10.1007/s10958-014-1846-7