Hypothesis testing with estimation-dependent costs and ∊-contamination prior

This paper mainly concerns about the binary hypothesis testing problems with unknown parameters in null hypothesis and alternative hypothesis, where the prior for unknown parameters is not completely known, but is assumed to belong to an ϵ-contamination class. We develop a method that decides between null hypothesis and alternative hypothesis reliably. Furthermore, when it decides in favor of null hypothesis or alternative hypothesis, we also provide an accurate estimate of the related unknown parameters. Numerical examples show the advantages of new method we proposed, in comparison with the method dealing with the prior distribution without uncertainty.