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 : nonparametric regression, smoother, kernel, thin-plate splines, stopping rules
@article{PS_2014__18__483_0,
author = {Cornillon, Pierre-Andr\'e and Hengartner, N. W. and Matzner-L{\o}ber, E.},
title = {Recursive bias estimation for multivariate regression smoothers},
journal = {ESAIM: Probability and Statistics},
pages = {483--502},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013046},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2013046/}
}
TY - JOUR AU - Cornillon, Pierre-André AU - Hengartner, N. W. AU - Matzner-Løber, E. TI - Recursive bias estimation for multivariate regression smoothers JO - ESAIM: Probability and Statistics PY - 2014 SP - 483 EP - 502 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2013046/ DO - 10.1051/ps/2013046 LA - en ID - PS_2014__18__483_0 ER -
%0 Journal Article %A Cornillon, Pierre-André %A Hengartner, N. W. %A Matzner-Løber, E. %T Recursive bias estimation for multivariate regression smoothers %J ESAIM: Probability and Statistics %D 2014 %P 483-502 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2013046/ %R 10.1051/ps/2013046 %G en %F PS_2014__18__483_0
Cornillon, Pierre-André; Hengartner, N. W.; Matzner-Løber, E. Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 483-502. doi : 10.1051/ps/2013046. http://archive.numdam.org/articles/10.1051/ps/2013046/
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