Detection of sparse additive functions
Open Access
- 1 January 2012
- journal article
- research article
- Published by Institute of Mathematical Statistics in Electronic Journal of Statistics
- Vol. 6 (none), 1409-1448
- https://doi.org/10.1214/12-ejs715
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.Keywords
Other Versions
This publication has 15 references indexed in Scilit:
- Variable selection in nonparametric additive modelsThe Annals of Statistics, 2010
- Detection boundary in sparse regressionElectronic Journal of Statistics, 2010
- Classification of sparse high-dimensional vectorsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
- Simultaneous analysis of Lasso and Dantzig selectorThe Annals of Statistics, 2009
- Estimation and confidence sets for sparse normal mixturesThe Annals of Statistics, 2007
- Estimation and detection of high-variable functions from Sloan—Woźniakowski spaceMathematical Methods of Statistics, 2007
- Compressed sensingIEEE Transactions on Information Theory, 2006
- Higher criticism for detecting sparse heterogeneous mixturesThe Annals of Statistics, 2004
- Nonparametric Goodness-of-Fit Testing Under Gaussian ModelsPublished by Springer Science and Business Media LLC ,2003
- Additive Regression and Other Nonparametric ModelsThe Annals of Statistics, 1985