Electronic Journal of Statistics

Detection of sparse additive functions

Ghislaine Gayraud and Yuri Ingster

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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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1409-1448.

Dates
First available in Project Euclid: 31 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1346421599

Digital Object Identifier
doi:10.1214/12-EJS715

Mathematical Reviews number (MathSciNet)
MR2988453

Zentralblatt MATH identifier
1295.62062

Subjects
Primary: 62H15: Hypothesis testing 60G15: Gaussian processes 62G10: Hypothesis testing 62G20: Asymptotic properties 60C20

Keywords
High-dimensional setting sparsity asymptotic minimax approach detection boundary Gaussian white noise model

Citation

Gayraud, Ghislaine; Ingster, Yuri. Detection of sparse additive functions. Electron. J. Statist. 6 (2012), 1409--1448. doi:10.1214/12-EJS715. https://projecteuclid.org/euclid.ejs/1346421599


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