Recursive Bias estimation for multivariate regression smoothers

Pierre-André Cornillon (1) , Nicolas W. Hengartner (2) , Eric Matzner-Løber (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LANL - Los Alamos National Laboratory

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.

Mots clés: stopping rules; thin-plate splines; kernel; smoother; nonparametric regression

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre-André Cornillon, Nicolas W. Hengartner, Eric Matzner-Løber. Recursive Bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, 2014, 18, pp.483-502. ⟨10.1051/ps/2013046⟩. ⟨hal-00955865⟩