Robust Kernel Estimator For Densities Of Unknown
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.
|Date of creation:||Sep 2006|
|Date of revision:|
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- Pagan,Adrian & Ullah,Aman, 1999.
Cambridge University Press, number 9780521586115.
- 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.
- 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.
- 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.
- Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
- 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).
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