Optimal minimax rates against nonsmooth alternatives
非光滑备择下的最优极小极大速率
Summary This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of nonsmooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is $n^{-1/4}$, where n is the sample size. The rate is…