Kernel method for overlapping coefficients estimation

Abstract

Most studies of estimating overlapping coefficients assume two specific parametric models for population densities. The methods that used such of this assumption are called parametric methods, which work well when these model assumptions are valid. Violation of parametric model assumption often leads to a poor estimation. The alternative nonparametric methods are more flexible than the parametric one and they required no assumptions about the parametric structure of population densities. Recently, some efforts were introduced to estimate the overlapping coefficients non-parametrically. In this paper, we introduced the nonparametric kernel method to estimate the three overlapping coefficients that known in the literature as Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure Δ. As the simulation results shown and based on the relative root mean square error (RRMSE) measure, if the two population distributions are assumed to be known then the parametric method performs better than the nonparametric kernel method. If there is no information about the structural form of the population distributions then the performance of the kernel method is very acceptable and it performs better than the parametric one.