Detection Boundary in Sparse Regression

Yu Ingster, Alexandre Tsybakov and N Verzelzn
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Yu Ingster: Crest
N Verzelzn: Crest

No 2010-28, Working Papers from Center for Research in Economics and Statistics

Abstract: 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.

Pages: 49
Date: 2010
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Citations: View citations in EconPapers (7)

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