A new Family of Hybrid Classical Polynomial Kernels in Density Estimation

International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume VI, Issue I, January 2021 | ISSN 2454–6186

A new Family of Hybrid Classical Polynomial Kernels in Density Estimation

  Benson Ade Afere
Department of Mathematics and Statistics,
Federal Polytechnic, Idah, Nigeria

Abstract – Kernel density estimation over the years has been placing more emphasis on the problem of the choice of optimal bandwidth. Nonetheless, the kernel function still has some roles to perform in the curve smoothing settings. Thus, in this paper, a new family of hybrid polynomial kernels is proposed. A generalized error scheme of the proposed family of kernels is constructed. A Monte Carlo experiment is performed using three univariate densities and it was discovered that the proposed family of hybrid polynomial kernels have significant low asymptotic mean integrated square error as compared with the existing family of polynomial kernels in the literature especially as the order of the kernels increases. Four real life data sets were equally used to show the performance of the proposed new family. It was observed that the proposed hybrid kernels perform well for the data sets considered.

Keywords – Kernel density estimation, polynomial kernels, hybrid kernels, generalized global error, Monte Carlo experiment.

MSC 2010 Classification: 62G07

I. INTRODUCTION

One class of smoothing techniques used for data analysis and visualizations is the nonparametric kernel density estimator (NKDE). This method is essentially the construction of an estimate of an underlying probability density function from an observed data set. This method has been used vastly in many areas such as in random differential equations problems [12], insurance [14], archeology, banking, climatology, economics, genetics, hydrology and physiology [17]. Its vast usability is based mainly on the simpleness of its implementation and interpretation of results [18]. It has been widely asserted that NKDE method is essentially marred majorly by the difficulties that centered around the choice of optimal bandwidth and minorly by the kernel functions [19]. Nevertheless, this does not undermine the choice and even the development of kernel functions [1]. In view of this, a family of hybrid polynomial kernels is proposed in this work.

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