A Criterion for the Fuzzy Set Estimation of the Regression Function. (2nd September 2012)

• Record Type: Journal Article
• Authors: Fajardo, Jesús A.
• Other Names: Thavaneswaran A. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2012(2012)
• Publication Date: 2012-09-02
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2012/593036
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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.