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Finite sample efficiency of the Gaussian kernel

Olga Y. Savchuk


For the most popular kernels in kernel density estimation and nonparametric regression the asymptotic efficiencies are close to one. In this study we assess the finite sample efficiency of the Gaussian kernel φ in the kernel density estimation context. For a wide range of
sample sizes and variety of the normal mixture densities, the empirical efficiencies of φ are shown to be about as high or even higher than the asymptotic value of 0.9512. Moreover, for each considered density the observed efficiencies tend to be higher for smaller sample
sizes. This reassures that using Phi at any sample size guarantees obtaining a highly efficient smooth estimate.


kernel density estimation, kernel regression, asymptotic kernel efficiency.

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