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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/593036 |
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| _version_ | 1832564271186182144 |
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| author | Jesús A. Fajardo |
| author_facet | Jesús A. Fajardo |
| author_sort | Jesús A. Fajardo |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-819ca28fee184c5f92ed44df53d9649d |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-819ca28fee184c5f92ed44df53d9649d2025-02-03T01:11:22ZengWileyJournal 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 |
| spellingShingle | Jesús A. Fajardo A Criterion for the Fuzzy Set Estimation of the Regression Function Journal of Probability and Statistics |
| title | 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_short | A Criterion for the Fuzzy Set Estimation of the Regression Function |
| title_sort | criterion for the fuzzy set estimation of the regression function |
| url | http://dx.doi.org/10.1155/2012/593036 |
| work_keys_str_mv | AT jesusafajardo acriterionforthefuzzysetestimationoftheregressionfunction AT jesusafajardo criterionforthefuzzysetestimationoftheregressionfunction |