Comparison of the Mean Square Errors of the Fuzzy Set Regression Estimator and Local Linear Regression Smoothers
In this paper we propose a criterion to obtain a reduction of the pointwise asymptotic mean square error of the fuzzy set regression estimator regarding the pointwise asymptotic mean square error of the local linear regression smoothers. This reduction shows that the fuzzy set regression estimator has better performance than the local linear regression smoothers, which is obtained by the conditions imposed on the thinning function, where this function allows us to define the fuzzy set regression estimator. Moreover, the theoretical finding is illustrated by means of two examples.
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