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August 2014 A criterion for the fuzzy set estimation of the density function
Jesús A. Fajardo
Braz. J. Probab. Stat. 28(3): 301-312 (August 2014). DOI: 10.1214/12-BJPS208


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.


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Jesús A. Fajardo. "A criterion for the fuzzy set estimation of the density function." Braz. J. Probab. Stat. 28 (3) 301 - 312, August 2014.


Published: August 2014
First available in Project Euclid: 17 July 2014

zbMATH: 1304.62075
MathSciNet: MR3263049
Digital Object Identifier: 10.1214/12-BJPS208

Keywords: Density estimation , fuzzy set estimation , nonparametric estimation

Rights: Copyright © 2014 Brazilian Statistical Association


Vol.28 • No. 3 • August 2014
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