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Recursive bias estimation for multivariate regressionsmoothers

Published online by Cambridge University Press:  10 October 2014

Pierre-André Cornillon ,
N. W. Hengartner  and
E. Matzner-Løber
Pierre-André Cornillon
Affiliation:
IRMAR, UMR 6625, Univ. Rennes 2, 35043 Rennes, France
N. W. Hengartner
Affiliation:
Stochastics Group, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
E. Matzner-Løber
Affiliation:
Lab. Mathématiques Appliquées, Agrocampus Ouest et Univ. Rennes 2, 35043 Rennes, France. [email protected]
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Abstract

This paper presents a practical and simple fully nonparametric multivariate smoothingprocedure that adapts to the underlying smoothness of the true regression function. Ourestimator is easily computed by successive application of existing base smoothers (withoutthe need of selecting an optimal smoothing parameter), such as thin-plate spline or kernelsmoothers. The resulting smoother has better out of sample predictive capabilities thanthe underlying base smoother, or competing structurally constrained models (MARS, GAM) forsmall dimension (3 ≤ d ≤7) and moderate sample size n ≤ 1000. Moreover our estimator is still usefulwhen d > 10and to our knowledge, no other adaptive fully nonparametric regression estimator isavailable without constrained assumption such as additivity for example. On a realexample, the Boston Housing Data, our method reduces the out of sample prediction error by20%. An R package ibr, available at CRAN, implements the proposedmultivariate nonparametric method in R.

Keywords

nonparametric regressionsmootherkernelthin-plate splinesstopping rules
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 483 - 502
Copyright
© EDP Sciences, SMAI 2014

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