Empirical likelihood method for complete independence test on high-dimensional data
Empirical likelihood method for complete independence test on high-dimensional data
复制标题
DOI：
10.1080/00949655.2022.2029860
复制
发表时间：
2022-01
影响因子：
1.2
通讯作者：
Y. Qi;Y. Zhou
中科院分区：
文献类型：
--
作者：
Y. Qi;Y. Zhou
给定来自p维随机向量的大小为n的随机样本，我们感兴趣的是测试随机向量的p个分量是否相互独立。这就是所谓的完全独立性测试。在多元正态情况下，它等价于测试相关矩阵是否是单位矩阵。本文提出了一种基于平方样本相关系数的完全独立性检验的单侧经验似然方法。本文证明了当n和p都趋于无穷大时，我们的单侧经验似然检验统计量的极限分布是，其中Z是一个标准正态随机变量。为了提高经验似然检验统计量的功效，我们还引入了一种重标度的经验似然检验统计量。我们进行了广泛的模拟研究，比较的重新缩放的经验似然方法和其他两个统计的性能。
Given a random sample of size n from a p dimensional random vector, we are interested in testing whether the p components of the random vector are mutually independent. This is the so-called complete independence test. In the multivariate normal case, it is equivalent to testing whether the correlation matrix is an identity matrix. In this paper, we propose a one-sided empirical likelihood method for the complete independence test based on squared sample correlation coefficients. The limiting distribution for our one-sided empirical likelihood test statistic is proved to be when both n and p tend to infinity, where Z is a standard normal random variable. In order to improve the power of the empirical likelihood test statistic, we also introduce a rescaled empirical likelihood test statistic. We carry out an extensive simulation study to compare the performance of the rescaled empirical likelihood method and two other statistics.