Iterative bias reduction multivariate smoothing in R: The ibr package
Abstract
In multivariate nonparametric analysis, sparseness of the covariates also called 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 oversmoothing 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 packages: NadarayaWatson kernel smoothers and thin plate splines smoothers. 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 RxR and the original Los Angeles ozone dataset.
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 arXiv:
 arXiv:1105.3605
 Bibcode:
 2011arXiv1105.3605C
 Keywords:

 Statistics  Computation
 EPrint:
 20 pages, 7 figures