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Journal Articles IEEE Transactions on Signal Processing Year : 2013

## Random Distortion testing and optimality of thresholding testes

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Dominique Pastor

#### Abstract

This paper addresses the problem of testing whether the Mahalanobis distance between a random signal $\Theta$ and a known deterministic model $\theta_0$ exceeds some given non-negative real number or not, when $\Theta$ has unknown probability distribution and is observed in additive independent Gaussian noise with positive definite covariance matrix. When $\Theta$ is deterministic unknown, we prove the existence of thresholding tests on the Mahalanobis distance to $\theta_0$ 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 $\theta_0$ 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 mistmatches, \mccp~tests can guarantee a specified false alarm probability, in contrast to standard Neyman-Pearson tests that may not respect this constraint.

### Dates and versions

hal-00952461 , version 1 (26-02-2014)

### Identifiers

• HAL Id : hal-00952461 , version 1

### Cite

Dominique Pastor, Quang Thang Nguyen. Random Distortion testing and optimality of thresholding testes. IEEE Transactions on Signal Processing, 2013, 61 (16), pp.4161 - 4171. ⟨hal-00952461⟩

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