We suggest a method for monotonizing general kernel-type
estimators, for example local linear estimators and Nadaraya .Watson
estimators. Attributes of our approach include the fact that it produces smooth
estimates, indeed with the same smoothness as the unconstrained estimate. The
method is applicable to a particularly wide range of estimator types, it can be
trivially modified to render an estimator strictly monotone and it can be
employed after the smoothing step has been implemented. Therefore,an
experimenter may use his or her favorite kernel estimator, and their favorite
bandwidth selector, to construct the basic nonparametric smoother and then use
our technique to render it monotone in a smooth way. Implementation involves
only an off-the-shelf programming routine. The method is based on maximizing
fidelity to the conventional empirical approach, subject to monotonicity.We
adjust the unconstrained estimator by tilting the empirical distribution so as
to make the least possible change, in the sense of a distance measure, subject
to imposing the constraint of monotonicity.