Generalised kernel density estimator

Novak, Serguei ORCID: https://orcid.org/0000-0001-7929-7641 (1999) Generalised kernel density estimator. Theory of Probability and Its Applications, 44 (3) . pp. 570-583. ISSN 0040-585X [Article] (doi:10.1137/S0040585X97977781)

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Abstract

We introduce a new class of nonparametric density estimators. It includes the classical kernel density estimator as well as the popular Abramson's estimator. We show that generalized estimators may perform much better than the classical one if the distribution has a heavy tail. The asymptotics of the mean squared error (MSE), optimal (in a sense) kernel, and smoothing parameter are found.

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