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 $\rho ,$ Morisita’s measure $\lambda$ and Weitzman’s measure $\Delta .$ 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.

摘要

大多数估计重叠系数的研究都假设人口密度有两个特定的参数模型。使用这种假设的方法称为参数方法，当这些模型假设有效时，它会很好地工作。违反参数模型假设通常会导致估计不佳。另一种非参数方法比参数方法更灵活，它们不需要关于人口密度的参数结构的假设。最近，引入了一些努力来以非参数方式估计重叠系数。在本文中，我们引入了非参数核方法来估计文献中称为 Matusita 测度的三个重叠系数$\rho ,$森田的措施$\lambda$和韦茨曼的度量$\Delta .$如模拟结果所示并基于相对均方根误差 (RRMSE) 测量，如果假设两个总体分布已知，则参数方法的性能优于非参数核方法。如果没有关于总体分布的结构形式的信息，那么核方法的性能是可以接受的，并且比参数方法的性能更好。