Abstract
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 Burr et al. (IEEE Trans Nucl Sci 57:2831–2840, 2010) 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.
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Hengartner, N., Matzner-Løber, E., Rouvière, L., Burr, T. (2018). Multiplicative Bias Corrected Nonparametric Smoothers. In: Bertail, P., Blanke, D., Cornillon, PA., Matzner-Løber, E. (eds) Nonparametric Statistics. ISNPS 2016. Springer Proceedings in Mathematics & Statistics, vol 250. Springer, Cham. https://doi.org/10.1007/978-3-319-96941-1_3
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