ESTIMATION OF REALIZED SIGNAL TO NOISE RATIO FOR A PAIR OF MULTIVARIATE SIGNALS |
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Authors: | Ravindra Khattree Rameshwar D Gupta |
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Institution: | BF Goodrich Chemical Group, P.O. Box 122, Avon Lake OH44012, USA;Div. Math, Engineering and Computer Science, University of New Brunswick, Saint John, NB, E2L 4L5, Canada. |
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Abstract: | Consider the case of classifying an incoming message as one of two known p-dimension signals or as a pure noise. Let the noise co-variance matrix (assumed to be same in all the three cases) be unknown. We consider the problem of estimation of “realized signal to noise ratio matrix”, which is an index of discriminatory power, under various loss functions. Optimum estimators are obtained under these loss functions. Finally, an attempt is made to provide a lower confidence bound for the realized signal to noise ratio matrix. In the process, the probability distribution of the smaller eigenvalue of a 2 × 2 confluent hypergeometric random matrix is obtained. |
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Keywords: | Confluent hypergeometric distribution Mahalanobis distance matrix signal to noise ratio matrix |
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