Journal of Probability and Statistics
Volume 2012 (2012), Article ID 593036, 18 pages
Research Article

A Criterion for the Fuzzy Set Estimation of the Regression Function

Departamento de Matemáticas, Universidad de Oriente, Cumaná 6101, Venezuela

Received 1 May 2012; Accepted 30 June 2012

Academic Editor: A. Thavaneswaran

Copyright © 2012 Jesús A. Fajardo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a criterion to estimate the regression function by means of a nonparametric and fuzzy set estimator of the Nadaraya-Watson type, for independent pairs of data, obtaining a reduction of the integrated mean square error of the fuzzy set estimator regarding the integrated mean square 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.