Multivariate nonparametric smoothers, such as kernel based smoothers and thin plate splines smoothers, are adversely impacted by the sparseness of data in high dimension, also known as the curse of dimensionality. Adaptive smoothers, that can exploit the underlying smoothness of the regression function, may partially mitigate this effect. This paper presents a comparative simulation study of a novel adaptive smoother (IBR) with competing multivariate smoothers available as package or function within the R language and environment for statistical computing. Comparison between the methods are made on simulated datasets of moderate size, from 50 to 200 observations, with two, five or 10 potential explanatory variables, and on a real dataset. The results show that the good asymptotic properties of IBR are complemented by a very good behavior on moderate sized datasets, results which are similar to those obtained with Duchon low rank splines.
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We would like to thank the associate editor and the referees for very valuable remarks and for pointing out to us the work of Duchon (1977).
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Cornillon, P., Hengartner, N., Jegou, N. et al. Iterative bias reduction: a comparative study. Stat Comput 23, 777–791 (2013). https://doi.org/10.1007/s11222-012-9346-4
- Multivariate smoothing
- Thin-plate splines
- Duchon splines
- Kernel regression
- Iterative bias reduction