Detection of sparse additive functions

2010/11/29 by Ghislaine Gayraud, Gayraud, Ghislaine, Yuri I. Ingster +1 · 2 citations
Mathematics · Economics, Econometrics and Finance · #Statistical Methods and Inference #Advanced Statistical Methods and Models #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.1011.6369

Abstract

We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection problem is expressed in terms of a nonparametric hypothesis testing problem and it is solved according to the asymptotical minimax approach. The minimax test procedures are adaptive in the sparsity parameter for high sparsity case. We extend to the functional case the known results in the detection of sparse high-dimensional vectors. In particular, our asymptotic detection boundaries are derived from the same asymptotic relations as in the vector case.

Citations

• Minimax-optimal rates for sparse additive models over kernel classes via convex programming

Cited by

• Adaptive almost full recovery in sparse nonparametric models
• Statistical inference in compound functional models

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