One Value of Smoothing Parameter vs Interval of Smoothing Parameter Values in Kernel Density Estimation

Aleksandra Katarzyna Baszczyńska

doi:10.18778/0208-6018.332.05

Authors

Aleksandra Katarzyna Baszczyńska University of Łódź, Faculty of Economics and Sociology, Department of Statistical Methods

DOI:

https://doi.org/10.18778/0208-6018.332.05

Keywords:

kernel density estimation, smoothing parameter, ad hoc methods

Abstract

Ad hoc methods in the choice of smoothing parameter in kernel density estimation, although often used in practice due to their simplicity and hence the calculated efficiency, are characterized by quite big error. The value of the smoothing parameter chosen by Silverman method is close to optimal value only when the density function in population is the normal one. Therefore, this method is mainly used at the initial stage of determining a kernel estimator and can be used only as a starting point for further exploration of the smoothing parameter value. This paper presents ad hoc methods for determining the smoothing parameter. Moreover, the interval of smoothing parameter values is proposed in the estimation of kernel density function. Basing on the results of simulation studies, the properties of smoothing parameter selection methods are discussed.

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References

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