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The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations

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  • Kauermann, Göran
  • Müller, Marlene
  • Carroll, Raymond J.

Abstract

Stuetzle and Mittal (1979) for ordinary nonparametric kernel regression and Kauermann and Tutz (1996) for nonparametric generalized linear model kernel regression constructed estimators with lower order bias than the usual estimators, without the need for devices such as second derivative estimation and multiple bandwidths of different order. We derive a similar estimator in the context of local (multivariate) estimation based on estimating functions. As expected, this lower order bias is bought at a cost of increased variance. Surprisingly, when compared to ordinary kernel and local linear kernel estimators, the bias-corrected estimators increase variance by a factor independent of the problem, depending only on the kernel used. The variance increase is approximately 40% and more for kernels in standard use. However, the variance increase is still less than that incurred when undersmoothing a local quadratic regression estimator.

Suggested Citation

  • Kauermann, Göran & Müller, Marlene & Carroll, Raymond J., 1998. "The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 41-47, January.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:1:p:41-47
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    1. Hardle, W. & Marron, J., 1989. "Bootstrap Simultaneous Error Bars For Nonparametric Regression," LIDAM Discussion Papers CORE 1989023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    2. Wenzhuan Zhang & Yingcun Xia, 2012. "Twicing local linear kernel regression smoothers," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 399-417.
    3. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Robust Kernel Estimator For Densities Of Unknown," Departmental Working Papers 2005-05, McGill University, Department of Economics.

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