JSM 2011 Online Program

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Abstract Details

Activity Number: 359
Type: Contributed
Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
Sponsor: Biometrics Section
Abstract - #303421
Title: High-Dimensional Sparse Multivariate Normal Mean Testing
Author(s): Rajarshi Mukherjee*+
Companies: Harvard University
Address: , , 02120,
Keywords: Higher Criticism ; Optimal detection Boundary ; High Dimensional Sparse Multivariate Normal Mean Testing ; Bahadur Efficiency
Abstract:

In High Dimensional Sparse Multivariate Normal Mean Testing problem, we have suggested a family of test statistics which, for a particular subset of the alternatives, mimics the oracle(that is the case where one knows the location of the possible signals) Likelihood Ratio Test in some "appropriate asymptotic" sense. Since the Likelihood Ratio Test, in the case one knows the exact location of the possible signals, can be considered optimal in the sense of Bahadur efficiency etc., it might seem reasonable to mimic it in "appropriate asymptotic" sense. The family of test statistics suggested is compared against the Higher Criticism Test statistic introduced by Donoho and Jin, and against the Optimal Detection Boundary as introduced by Ingster for the testing problem in question. The correlated case was also considered.


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