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2000•Theory of Probability and Its ApplicationsRequires access

Generalized Kernel Density Estimator

S. Y. Novak

Open publisher page 11 citations

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.

About this research paper

What this paper is about

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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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

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Method / approach

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Available 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.

Key concepts: Mathematics, Estimator, Kernel density estimation, Mean squared error, Multivariate kernel density estimation, Applied mathematics, Kernel (algebra), Kernel smoother

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