Robust Decision Design Using a Distance Criterion

An alternate formulation of the robust hypothesis testing problem is considered in which robustness is defined in terms of a maximin game with a statistical distance criterion as a payoff function. This distance criterion, which is a generalized version of signal-to-noise ratio, offers advantages over traditional error probability or risk criteria in this problem because of the greater tractability of the distance measure. Within this framework, a design procedure is developed which applies to a more general class of problems than do earlier robustness results based on risks. Furthermore, it is shown for the general case that when a decision rule exists that is robust in terms of risk, the same decision rule will be robust in terms of distance, a fact which supports the use of the latter criterion.