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The usual second order nonparametric kernel estimators are of wide uses in data analysis and visualization but constrained with slow convergence rate. Higher order kernels provide a faster convergence rates and are known to be bias reducing kernels. In this paper, we propose a hybrid of the fourth order kernel which is a merger of two successive fourth order kernels and the statistical properties of these hybrid kernels were study. The results of our simulation reveals that the proposed higher order hybrid kernels outperformed their corresponding parent’s kernel functions using the asymptotic mean integrated squared error.

On Hybridizations of Fourth Order Kernel of the Beta Polynomial Family.