Random Distortion Testing and Applications
Résumé
We address Random Distortion Testing (rdt), that is, the problem of testing whether the Mahalanobis distance between a random signal $\Theta$ and a known deterministic model $\theta_0$ exceeds some given $\tau \geqslant 0$ or not, when $\Theta$ has unknown probability distribution and is observed in additive independent Gaussian noise with positive definite covariance matrix. A suitable optimality criterion for \rdt is presented and theoretical results on optimal tests for this criterion are given. Several applications of these results are presented and analyzed. They address the detection of signals in case of model mismatch and the detection of deviations from model $\theta_0$.