Notes on the Performance of the Boundary Locally Adaptive Kernel and Boundary Fuzzy Set Density Estimators

https://doi.org/10.5281/zenodo.7487484

• Jesús A. Fajardo Departamento de Matemática del Núcleo de Sucre, Universidad de Oriente

Keywords: Fuzzy set density estimator, boundary estimation, adaptive kernel density estimator

Abstract

These notes provide a new result related to the nonparametric density function estimation problem, not based on kernels, which allows to extend the scope of the fuzzy set density estimator. For it, the new boundary fuzzy set density estimator is considered to compare its performance with the performance of the boundary locally adaptive kernel density estimator. Each performance is obtained by considering four forms of specific densities and two real datasets. Simulations show that the boundary fuzzy set estimator has better performance at points near 0, in a bn spread neighborhood, when it is compared with the performance of the boundary locally adaptive kernel estimator, for the four shapes of densities considered. The parameter b n is the smoothing parameter of the boundary fuzzy set estimator.