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Bandwidth choice for robust nonparametric scale function estimation

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  • Boente, Graciela
  • Ruiz, Marcelo
  • Zamar, Ruben H.

Abstract

We introduce and compare several robust procedures for bandwidth selection when estimating the variance function. These bandwidth selectors are to be used in combination with the robust scale estimates introduced by Boente et al. (2010a). We consider two different robust cross-validation strategies combined with two ways for measuring the cross-validation prediction error. The different proposals are compared with non robust alternatives using Monte Carlo simulation. We also derive some asymptotic results to investigate the large sample performance of the corresponding robust data-driven scale estimators.

Suggested Citation

  • Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2012. "Bandwidth choice for robust nonparametric scale function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1594-1608.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1594-1608
    DOI: 10.1016/j.csda.2011.10.002
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    References listed on IDEAS

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    1. Ana Bianco & Graciela Boente, 2007. "Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 274-306, March.
    2. Levine, M., 2006. "Bandwidth selection for a class of difference-based variance estimators in the nonparametric regression: A possible approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3405-3431, August.
    3. Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2010. "On a robust local estimator for the scale function in heteroscedastic nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1185-1195, August.
    4. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    5. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
    6. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    7. Holger Dette & Mareen Marchlewski, 2010. "A robust test for homoscedasticity in nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 723-736.
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