Density Estimation using a Modified Multivariate Cluster Sampling Kernel Approach

Abstract

This work is based on the use of the modified multivariate cluster sampling kernel density estimation (MMCKDE). The method is demonstrated using the Nigerian crime rate data reported to the Police as contained in the publication of the National Bureau of Statistics in 2009. The method is data-driven. The quality of the estimates from the MMCKDE method showed some significant improvements over the fixed H smoothing and the multivariate cluster sampling kernel density estimation methods in terms of the variance and the asymptotic mean squared error.