A note on nonparametric density deconvolution by weighted kernel estimators

Abstract

Abstract Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimatorfor the deconvolution problem. In the case of Gaussian kernels and measurement er-ror, they argued that the weighted kernel density estimator is a competitive estimatorover the classical deconvolution kernel estimator. In this paper we consider weightedkernel density estimators when sample observations are contaminated by double expo-nentially distributed errors. The performance of the weighted kernel density estimatorsis compared over the classical deconvolution kernel estimator and the kernel density es-timator based on the support vector regression method by means of a simulation study.The weighted density estimator with the Gaussian kernel shows numerical instabilityin practical implementation of optimization function. However the weighted densityestimates with the double exponential kernel has very similar patterns to the classicalkernel density estimates in the simulations, but the shape is less satisfactory than theclassical kernel density estimator with the Gaussian kernel.Keywords: Deconvolution, kernel density estimator, support vector regression, weightedkernel density estimator.