Iterative bias reduction multivariate smoothing in R: The ibr package

TL;DR

The paper introduces the ibr R package that iteratively reduces bias in multivariate smoothing estimators, addressing the curse of dimensionality by over-smoothing and bias correction.

Contribution

It presents a novel bias correction method for multivariate smoothers and implements it in the ibr package, with practical stopping rules and applications.

Findings

Effective bias reduction demonstrated on toy and real datasets

Applicable to Nadaraya-Watson and thin plate spline smoothers

Provides practical tools for bias correction in high-dimensional smoothing

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 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 packages: Nadaraya-Watson 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.