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Particular Performance Between the Fuzzy Set and Univariate Balloon Estimators of the Density Function

Jesús A. Fajardo

Abstract



In this paper we propose a criterion to estimate the density function by means of a nonparametric and fuzzy set estimator, based on n i.i.d random variable, obtaining a reduction of the asymptotic mean integrated square error of the fuzzy set estimator regarding the
asymptotic mean integrated square error of the univariate balloon estimator for all order-p kernels. This reduction shows that the fuzzy set estimator has better performance than the univariate balloon estimator. Finally, these theoretical findings are illustrated using a
numerical example.

Keywords


Fuzzy Set Estimator, Adaptive Kernel Estimator

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