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Allthough nonparametric kernel density estimation with bias reduce isnowadays a standard technique in explorative data-analysis, there is still abig dispute on how to assess the quality of the estimate and which choice ofbandwidth is optimal. This article examines the most important bandwidthselection methods for kernel density estimation with bias reduce, inparticular, normal reference, least squares cross-validation, biasedcrossvalidation and $\beta$-Divergence loss. Methods are described andexpressions are presented. We will compare these various bandwidth selector onsimulated data. As an example of real data, we will use econometric data setsCO2 per capita in example 1 and the second

$\beta$-Divergence loss for the kernel density estimation with bias reduced