TY - GEN
T1 - Multiplicative bias corrected nonparametric smoothers
AU - Hengartner, N.
AU - Matzner-Løber, E.
AU - Rouvière, L.
AU - Burr, T.
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85069994241
U2 - 10.1007/978-3-319-96941-1_3
DO - 10.1007/978-3-319-96941-1_3
M3 - Conference contribution
AN - SCOPUS:85069994241
SN - 9783319969404
T3 - Springer Proceedings in Mathematics and Statistics
SP - 31
EP - 52
BT - Nonparametric Statistics- 3rd ISNPS 2016
A2 - Bertail, Patrice
A2 - Blanke, Delphine
A2 - Cornillon, Pierre-André
A2 - Matzner-Løber, Eric
PB - Springer New York LLC
T2 - 3rd Conference of the International Society for Nonparametric Statistics, ISNPS 2016
Y2 - 11 June 2016 through 16 June 2016
ER -