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Robust Kernel Estimator For Densities Of Unknown

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  • Yulia Kotlyarova

    ()

  • Victoria Zinde-Walsh

    ()

Abstract

Results on nonparametric kernel estimators of density differ according to the assumed degree of density smoothness; it is often assumed that the density function is at least twice differentiable. However, there are cases where non-smooth density functions may be of interest. We provide asymptotic results for kernel estimation of a continuous density for an arbitrary bandwidth/kernel pair. We also derive the limit joint distribution of kernel density estimators coresponding to different bandwidths and kernel functions. Using these reults, we construct an estimator that combines several estimators for different bandwidth/kernel pairs to protect against the negative consequences of errors in assumptions about order of smoothness. The results of a Monte Carlo experiment confirm the usefulness of the combined estimator. We demonstrate that while in the standard normal case the combined estimator has a relatively higher mean squared error than the standard kernel estimator, both estimators are highly accurate. On the other hand, for a non-smooth density where the MSE gets very large, the combined estimator provides uniformly better results than the standard estimator.

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Bibliographic Info

Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2005-05.

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Length: 29 pages
Date of creation: Sep 2006
Date of revision:
Handle: RePEc:mcl:mclwop:2005-05

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  1. Kauermann, Göran & Müller, Marlene & Carroll, Raymond J., 1997. "The efficiency of bias-corrected estimators for nonparametric kernel estimation based on local estimating equations," SFB 373 Discussion Papers 1997,70, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. PARK, Byeong & TURLACH, Berwin, 1992. "Practical performance of several data driven bandwidth selectors," CORE Discussion Papers 1992005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, 05.
  4. repec:fth:louvco:9205 is not listed on IDEAS
  5. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
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Cited by:
  1. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde‐Walsh, 2011. "Adapting kernel estimation to uncertain smoothness," LSE Research Online Documents on Economics 42015, London School of Economics and Political Science, LSE Library.
  2. SCHAFGANS, Marcia M.A. & ZINDE-WALSH, Victoria, 2007. "Robust Average Derivative Estimation," Cahiers de recherche 12-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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