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A Criterion for the Fuzzy Set Estimation of the Regression Function

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  • Jesús A. Fajardo

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.

Suggested Citation

  • Jesús A. Fajardo, 2012. "A Criterion for the Fuzzy Set Estimation of the Regression Function," Journal of Probability and Statistics, Hindawi, vol. 2012, pages 1-18, September.
    • Handle: RePEc:hin:jnljps:593036
    DOI: 10.1155/2012/593036
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    Cited by:

    1. Jesús Fajardo & Pedro Harmath, 2021. "Boundary estimation with the fuzzy set density estimator," METRON, Springer;Sapienza Università di Roma, vol. 79(3), pages 285-302, December.

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