• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.951-959
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• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.77-84
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• 2013

This paper deals with the relative efficiency of two kernel estimators $\hat{f}_n$ and $\hat{g}_n$ by using spherical data, as proposed by Park (2012), and Bai et al. (1988), respectively. For this, we suggest the computing flows for the relative efficiency on the 2-dimensional unit sphere. An evaluation procedure between two estimators (given the same kernels) is also illustrated through the observed data on normals to the orbital planes of long-period comets.