Some Improvements in Nonparametric Multivariate Kernel Density Estimation

Abstract

A popular technique of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a bandwidth (smoothing parameter H). It aid density estimation and pattern recognition. This paper presents new approaches in nonparametric density construction problem, particularly at the boundary points using the dataset and a pilot plot. However, since the main way to improve density estimation is to obtain a reduced mean squared error (MSE). When the MSE for these approaches were evaluated and compared. Some improvements were seen in two proposed approaches. These were achieved under a sufficiently smoothing technique in the existing approaches. These approaches are adaptive and they reduce under fitting and over fitting as the case may be of the data set and aid statistical inference.

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

“…2017). Currently, a variety of sophistication of the basic kernel estimator has been proposed, all pointing to the importance of adaptive kernel estimator (see Kathovnik and Shmulevich 2002, Salgado-Ugarte and Perez-Hernandez 2003, Zhang and Chan 2011, Yang et al 2019, Ogbeide and Osemwenkhae 2019. The "adaptive" nature of the density estimate arises from the varying bandwidth used in the estimation process.…”