Stable Detection of Signal That Is Not Precisely Known

The paper considers the testing of a simple hypothesis with a complex alternative. It is assumed that the alternative is specified as a class of densities within fixed boundaries; the minimax Neyman–Pearson rule is determined. This rule is applied to the problem of detecting a signal with unknown parameters, where it corresponds to replacement of the unknown parameters in the likelihood ratio by the maximum-likelihood estimate of the minimum-likelihood statistic. Examples are considered.