A density based empirical likelihood approach for testing bivariate normality.
A density based empirical likelihood approach for testing bivariate normality.
复制标题
用于测试二元正态性的基于密度的经验似然方法。
DOI：
10.1080/00949655.2018.1476516
复制
发表时间：
2018
影响因子：
1.2
通讯作者：
Vexler,Albert
中科院分区：
文献类型：
--
作者：
Gurevich,Gregory;Vexler,Albert
基于样本熵的测试，方法的筛选和Grenander估计类型的程序是已知的是非常有效的工具，用于评估正态性的基础数据分布，在一维非参数设置。最近，它已被证明，基于密度的经验似然（EL）的概念扩展和简化这些方法，提出了一个强大的方法近似最佳参数似然比检验统计量，在一个分布自由的方式。在本文中，我们讨论了困难相关的构造密度为基础的EL比技术，检验二元正态性，并提出了解决这个问题。为此，一种新的二元样本熵表达式推导和示出满足已知的概念相关的二元直方图密度估计。Monte Carlo结果表明，新的基于密度的EL比检验的二元正态性表现非常好的有限样本容量。为了证明所提出的方法的良好的适用性，我们展示了一个真实的数据的例子。
Sample entropy based tests, methods of sieves and Grenander estimation type procedures are known to be very efficient tools for assessing normality of underlying data distributions, in one-dimensional nonparametric settings. Recently, it has been shown that the density based empirical likelihood (EL) concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics, in a distribution-free manner. In this paper, we discuss difficulties related to constructing density based EL ratio techniques for testing bivariate normality and propose a solution regarding this problem. Toward this end, a novel bivariate sample entropy expression is derived and shown to satisfy the known concept related to bivariate histogram density estimations. Monte Carlo results show that the new density based EL ratio tests for bivariate normality behave very well for finite sample sizes. To exemplify the excellent applicability of the proposed approach, we demonstrate a real data example.