Title: A new second order kernel of the beta polynomial family in density estimation

Authors: Israel Uzuazor Siloko; Edith Akpevwe Siloko; Sunday Amaju Ojobor; Richard Oghenefejio Agwemuria; Cyril Chukwuka Ishiekwene; Osayomore Ikpotokin; Efosa Michael Ogbeide; Esosa Enoyoze

Addresses: Department of Mathematics, Edo State University Uzairue, Uzairue, 312102, Nigeria ' Department of Statistics, University Benin, Benin City, 300213, Nigeria ' Department of Mathematics, Delta State University of Science and Technology, Ozoro, 334111, Nigeria ' Department of Mathematics, Federal University of Petroleum Resources Effurun, Effurun, 330102, Nigeria ' Department of Statistics, University Benin, Benin City, 300213, Nigeria ' Department of Mathematics and Statistics, Ambrose Alli University, Ekpoma, 310101, Nigeria ' Department of Mathematics and Statistics, Ambrose Alli University, Ekpoma, 310101, Nigeria ' Department of Mathematics, Edo State University Uzairue, Uzairue, 312102, Nigeria

Abstract: Data exploratory analysis and data visualisations are the main functions of kernel density estimation. The kernel density estimation techniques depend fundamentally on the bandwidth that determines its smoothness and a kernel function. In this paper, a novel second order beta kernel from its classical counterpart with improved performance is introduced. The improvement of the newly introduced kernel family is ascribed to their possession of additional powers of derivatives since they are polynomial families. Although several techniques of kernel construction exist in literature, the proposed kernels were derived by modifying the additive higher order kernel construction rule. A real data and different sample sizes were employed in authenticating and validating the efficacy of the proposed kernels' performances using the asymptotic mean integrated squared error (AMISE) as the measure of accuracy. The results of the proposed kernels were compared with existing kernels with the proposed kernels outperforming the traditional kernels family.

Keywords: bandwidth; beta; density; estimation; kernel.

DOI: 10.1504/IJCSM.2024.143206

International Journal of Computing Science and Mathematics, 2024 Vol.20 No.4, pp.273 - 289

Received: 27 May 2023
Accepted: 18 Mar 2024
Published online: 09 Dec 2024 *

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