Characteristics of Robust Rules for Testing Two Hypotheses

The characteristics of a robust rule for testing two hypotheses are examined. We deal with the case where the alternative sets are neighborhoods of unknown multivariate probability distributions and a decision statistics is a censored version of the likelihood ratio. The decision rule is randomized. The results obtained are applied for a wide class of the alternative sets and can be useful for various problems of hypothesis testing and signal detection in noise. Some examples are considered.