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Abstract Details
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Activity Number:
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181
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Type:
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Contributed
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Date/Time:
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Monday, August 1, 2011 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #302612 |
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Title:
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Power of Roy's Largest Root Test in Testing for Signal in Noise
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Author(s):
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Iain M. Johnstone*+ and Boaz Nadler
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Companies:
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Stanford University and Weizmann Institute of Science
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Address:
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Department of Statistics, Stanford University, CA, 94305, USA
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Keywords:
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signal detection ;
Roy's largest root test ;
Matrix perturbation ;
Inverse Wishart distribution ;
MANOVA
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Abstract:
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We consider the problem of detecting the presence of a signal embedded in noise. It is assumed that we are given both signal bearing and noise-only samples, with Gaussian data in both samples. The problem reduces to either testing the equality of covariance matrices or testing for null regression against an alternative of a rank one perturbation. Using a matrix perturbation approach, combined with known results on the eigenvalues of inverse Wishart matrices, we study the behavior of the largest eigenvalue of the relevant matrix, and derive an approximate expression for the power of Roy's largest root test. The accuracy of our expressions is confirmed by simulations.
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