Brazilian Journal of Probability and Statistics

A criterion for the fuzzy set estimation of the density function

Jesús A. Fajardo

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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 integrated mean square error of the fuzzy set estimator regarding the integrated mean squared error of the classic kernel estimators. This reduction shows that the fuzzy set estimator has better performance than the kernel estimations. Also, the convergence rate of the optimal scaling factor is computed, which coincides with the convergence rate in classic kernel estimation. Finally, these theoretical findings are illustrated using a numerical example.

Article information

Braz. J. Probab. Stat., Volume 28, Number 3 (2014), 301-312.

First available in Project Euclid: 17 July 2014

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Density estimation fuzzy set estimation nonparametric estimation


Fajardo, Jesús A. A criterion for the fuzzy set estimation of the density function. Braz. J. Probab. Stat. 28 (2014), no. 3, 301--312. doi:10.1214/12-BJPS208.

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