Risk bounds in isotonic regression

Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform n-1/3-consistency of the ₚ risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.