Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, 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 for multivariate normal data based on squared sample correlation coefficients. The limiting distribution for our one-sided empirical likelihood test statistic is proved to be $Z^2I(Z>0)$ 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 which are related to the sum of squared sample correlation coefficients.

翻译：根据一个大小为10美元的随机随机矢量的随机抽样,其中美元值和美元值都很大,我们有兴趣测试随机矢量的美元组成部分是否相互独立。这是所谓的完全独立的测试。在多变量的正常情况下,它相当于测试相关性矩阵是否是一个身份矩阵。在本文中,我们提出了一个单向的经验性可能性方法,用于根据正方位样本相关系数对多变量正常数据进行全面独立测试。事实证明,我们单方经验性概率测试统计数据的有限分布为$2I( ⁇ 0),而美元和美元都倾向于不固定,而美元是一个标准的普通随机变量。为了提高经验性概率测试统计数据的力量,我们还引入了一种重新缩放的经验性概率测试统计。我们进行了广泛的模拟研究,以比较重新标定的经验性概率方法的性能以及与正方位样本相关系数之和有关的其他两项统计数据。