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 R2 and the original Los Angeles ozone dataset.