Abstract
Suppose that observations (t1, y1), …, (tn, yn) are collected from isotonic regression y = f(t) + ϵ, where f is a bounded non-increasing function. Denote by [ftilde]n be the isotonic estimate of f. This paper derives a nonasymptotic bound on the L2 risk of [ftilde]n for given n and f. This bound is then used to study both the limit of the L2 risk of [ftilde]n as n goes to infinity and the maximum of the L2 risk of [ftilde]n over a class of bounded non-increasing functions.