This paper presents a practical and simple fully nonparametric multivariate smoothing
procedure that adapts to the underlying smoothness of the true regression function. Our
estimator is easily computed by successive application of existing base smoothers (without
the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel
smoothers. The resulting smoother has better out of sample predictive capabilities than
the underlying base smoother, or competing structurally constrained models (MARS, GAM) for
small dimension (3 ≤ d ≤
7) and moderate sample size n ≤ 1000. Moreover our estimator is still useful
when d > 10
and to our knowledge, no other adaptive fully nonparametric regression estimator is
available without constrained assumption such as additivity for example. On a real
example, the Boston Housing Data, our method reduces the out of sample prediction error by
20%. An R package ibr, available at CRAN, implements the proposed
multivariate nonparametric method in R.