Feasible nonparametric estimation of multiargument monotone functions

This article presents a two-stage estimation procedure that uses an ad hoc but very easily implemented isotonization of a kernel estimator. This procedure yields an isotonic estimator with the convergence properties of the kernel estimator. Although the isotonization in the second stage does not satisfy the least squares condition, this hybrid estimator may be considered to be a multidimensional generalization of similar procedures for the one-dimensional case suggested by Friedman and Tibshirani and by Mukarjee. We derive some of the asymptotic properties of our estimator and demonstrate other statistical properties with Monte Carlo studies. We conclude by providing a real data example.