Detection of sparse additive functions

Abstract

We study the problem of detection of high-dimensional signal functions in the Gaussian white noise model. We assume that, in addition to a smoothness assumption, the signal function has an additive sparse structure. The detection problem is expressed in terms of a nonparametric hypothesis testing problem and is solved using asymptotically minimax approach. We provide minimax test procedures that are adaptive in the sparsity parameter in the high sparsity case. We extend some known results related to the detection of sparse high-dimensional vectors to the functional case. In particular, our derivation of asymptotic detection rates is based on same detection boundaries as in the vector case.