Random Distortion Testing and Optimality of Thresholding Tests
| Autor: | Dominique Pastor, Quang-Thang Nguyen |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | IEEE Transactions on Signal Processing. 61:4161-4171 |
| ISSN: | 1941-0476 1053-587X |
| DOI: | 10.1109/tsp.2013.2265680 |
| Popis: | This paper addresses the problem of testing whether the Mahalanobis distance between a random signal Θ and a known deterministic model θ0 exceeds some given non-negative real number or not, when Θ has unknown probability distribution and is observed in additive independent Gaussian noise with positive definite covariance matrix. When Θ is deterministic unknown, we prove the existence of thresholding tests on the Mahalanobis distance to θ0 that have specified level and maximal constant power (MCP). The MCP property is a new optimality criterion involving Wald's notion of tests with uniformly best constant power ( UBCP) on ellipsoids for testing the mean of a normal distribution. When the signal is random with unknown distribution, constant power maximality extends to maximal constant conditional power (MCCP) and the thresholding tests on the Mahalanobis distance to θ0 still verify this novel optimality property. Our results apply to the detection of signals in independent and additive Gaussian noise. In particular, for a large class of possible model mismatches, MCCP tests can guarantee a specified false alarm probability, in contrast to standard Neyman-Pearson tests that may not respect this constraint. |
| Databáze: | OpenAIRE |
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