A Criterion for the Fuzzy Set Estimation of the Regression Function

A Criterion for the Fuzzy Set Estimation of the Regression Function

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 o...

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Main Author: Jesús A. Fajardo
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2012/593036
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spelling doaj-819ca28fee184c5f92ed44df53d9649d2020-11-24T20:56:01ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/593036593036A Criterion for the Fuzzy Set Estimation of the Regression FunctionJesús A. Fajardo0Departamento de Matemáticas, Universidad de Oriente, Cumaná 6101, VenezuelaWe 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.http://dx.doi.org/10.1155/2012/593036
collection DOAJ
language English
format Article
sources DOAJ
author Jesús A. Fajardo
spellingShingle Jesús A. Fajardo
A Criterion for the Fuzzy Set Estimation of the Regression Function
Journal of Probability and Statistics
author_facet Jesús A. Fajardo
author_sort Jesús A. Fajardo
title A Criterion for the Fuzzy Set Estimation of the Regression Function
title_short A Criterion for the Fuzzy Set Estimation of the Regression Function
title_full A Criterion for the Fuzzy Set Estimation of the Regression Function
title_fullStr A Criterion for the Fuzzy Set Estimation of the Regression Function
title_full_unstemmed A Criterion for the Fuzzy Set Estimation of the Regression Function
title_sort criterion for the fuzzy set estimation of the regression function
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/593036
work_keys_str_mv AT jesusafajardo acriterionforthefuzzysetestimationoftheregressionfunction
AT jesusafajardo criterionforthefuzzysetestimationoftheregressionfunction
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