Iterative Bias Reduction Multivariate Smoothing in R : The ibr Package

Abstract : In multivariate nonparametric analysis curse of dimensionality forces one to use large smoothing parameters. This leads to a biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting base smoother has a small variance but a substantial bias. In this paper, we propose an R package named ibr to iteratively correct the initial bias of the (base) estimator by an estimate of the bias obtained by smoothing the residuals. After a brief description of iterated bias reduction smoothers, we examine the base smoothers implemented in the package: Nadaraya-Watson kernel smoothers, Duchon splines smoothers and their low rank counterparts. Then, we explain the stopping rules available in the package and their implementation. Finally we illustrate the package on two examples: a toy example in R 2 and the original Los Angeles ozone dataset.
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Article dans une revue
Journal of Statistical Software, University of California, Los Angeles, 2017, 77 (9), 〈10.18637/jss.v077.i09〉
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https://hal.archives-ouvertes.fr/hal-01533622
Contributeur : Marie-Annick Guillemer <>
Soumis le : mardi 6 juin 2017 - 16:07:49
Dernière modification le : mercredi 2 août 2017 - 10:11:13

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Pierre-André Cornillon, Nicolas Hengartner, Eric Matzner-Løber. Iterative Bias Reduction Multivariate Smoothing in R : The ibr Package. Journal of Statistical Software, University of California, Los Angeles, 2017, 77 (9), 〈10.18637/jss.v077.i09〉. 〈hal-01533622〉

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