Main Article Content


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.


Kernel Bandwidth AMISE Beta Polynomial Higher Order Kernel.

Article Details

Author Biographies

Israel Uzuazor SILOKO, Edo University Iyamho

Department of Mathematics and Computer Science

Lecturer I

Osayomore IKPOTOKIN, Ambrose Alli University, Ekpoma

Department of Mathematics and Statistics

Senior Lecturer

Edith Akpevwe SILOKO, University of Benin

Department of Mathematics

How to Cite
SILOKO, I. U., IKPOTOKIN, O., & SILOKO, E. A. (2019). On Hybridizations of Fourth Order Kernel of the Beta Polynomial Family. Pakistan Journal of Statistics and Operation Research, 15(3), 819-829.