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Multiplicative bias corrected nonparametric smoothers. (English) Zbl 1414.62132
Bertail, Patrice (ed.) et al., Nonparametric statistics. 3rd ISNPS, Avignon, France, June 2016. Seleced papers of the 3rd conference of the International Society for Nonparametric Statistics (ISNPS), Avignon, France, June 11–16, 2016. Cham: Springer. Springer Proc. Math. Stat. 250, 31-52 (2018).
Summary: This contribution presents a general multiplicative bias reduction strategy for nonparametric regression. The approach is most effective when applied to an oversmooth pilot estimator, for which the bias dominates the standard error. The practical usefulness of the method was demonstrated in [the authors, “Smoothing low resolution spectral data”, IEEE Trans. Nucl. Sci. 57, No. 5, 2831–2840 (2010; doi:10.1109/TNS.2010.2054110)] in the context of estimating energy spectra. For such data sets, it was observed that the method could decrease significantly the bias with only negligible increase in variance. This chapter presents the theoretical analysis of that estimator. In particular, we study the asymptotic properties of the bias corrected local linear regression smoother, and prove that it has zero asymptotic bias and the same asymptotic variance as the local linear smoother with a suitably adjusted bandwidth. Simulations show that our asymptotic results are available for modest sample sizes.
For the entire collection see [Zbl 1411.62017].
MSC:
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
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