Suppose that a target function is monotonic, namely, weakly increasing, and
an original estimate of the target function is available, which is not weakly
increasing. Many common estimation methods used in statistics produce such
estimates. We show that these estimates can always be improved with no harm
using rearrangement techniques: The rearrangement methods, univariate and
multivariate, transform the original estimate to a monotonic estimate, and the
resulting estimate is closer to the true curve in common metrics than the
original estimate.