Composite hypothesis testing by optimally distinguishable distributions

Relying on optimally distinguishable distributions (ODD), it was defined very recently a new framework for the composite hypothesis testing. We resort to the linear model to investigate the performances of the ODD detector and to compare it with the widely used generalized likelihood ratio test (GLRT). As the ODD concept is very new, its application to models with nuisance parameters was not discussed in the previous literature. The present study attempts to fill the gap by proposing a modified ODD criterion to accommodate the practical case of unknown noise variance.