Detection Boundary in Sparse Regression
We study the problem of detection of a p-dimensional sparse vector ofparameters in the linear regression model with Gaussian noise. We establishthe detection boundary, i.e., the necessary and sufficient conditions for thepossibility of successful detection as both the sample size n and the dimensionp tend to the infinity. Testing procedures that achieve this boundary arealso exhibited. Our results encompass the high-dimensional setting (p » n).The main message is that, under some conditions, the detection boundaryphenomenon that has been proved for the Gaussian sequence model, extendsto high-dimensional linear regression. Finally, we establish the detectionboundaries when the variance of the noise is unknown. Interestingly, thedetection boundaries sometimes depend on the knowledge of the variance ina high-dimensional setting.
|Date of creation:||2010|
|Date of revision:|
|Contact details of provider:|| Postal: 15 Boulevard Gabriel Peri 92245 Malakoff Cedex|
Phone: 01 41 17 60 81
Web page: http://www.crest.fr
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2010-28. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Florian Sallaberry)
If references are entirely missing, you can add them using this form.