Least favorable distributions for robust quickest change detection

We study the problem of robust quickest change detection where the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions. Both Bayesian and minimax versions of the quickest change detection problem are considered. When the uncertainty classes satisfy some specific conditions, we identify least favorable distributions (LFD´s) from the uncertainty classes, and show that the detection rule designed for the LFD´s is optimal in a minimax sense. The condition is similar to that required for the existence of LFD´s for the robust hypothesis testing problem studied by Huber.