In monotone regression procedures one utilizes only the monotonicity of the regression function. In nonparametric regression one utilizes only the assumed smoothness. The analytic and asymptotic properties of the estimator are superior in the latter case; however, monotonicity is not guaranteed. We study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators.
"Monotone Nonparametric Regression." Ann. Statist. 16 (2) 741 - 750, June, 1988. https://doi.org/10.1214/aos/1176350832