This paper presents a difference-type lower bound for the Bayes risk as a difference-type extension of the Borovkov-Sakhanenko bound. The resulting bound asymptotically improves the Bobrovsky-Mayor-Wolf-Zakai bound which is difference-type extension of the Van Trees bound. Some examples are also given.
Keywords: Bayes risk; Bobrovsky–Mayor–Wolf–Zakai bound; Borovkov–Sakhanenko bounds; Laplace approximation; Van Trees bound.