ROBUST KERNEL ESTIMATOR FOR DENSITIES OF UNKNOWN

Yulia Kotlyarova and Victoria Zinde-Walsh

Departmental Working Papers from McGill University, Department of Economics

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.

JEL-codes: C14 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2006-09
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:mcl:mclwop:2005-05

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