论文标题
在高维数据上完成独立测试的经验可能性方法
Empirical likelihood method for complete independence test on high dimensional data
论文作者
论文摘要
考虑到从$ p $ dimensional随机向量的随机样本$ n $，其中$ n $和$ p $都很大，我们有兴趣测试随机矢量的$ p $组件是否相互独立。这是所谓的完整独立测试。在多元正常情况下，它等效于测试相关矩阵是否是身份矩阵。在本文中，我们提出了一种基于平方样品相关系数的多元正常数据的完整独立性测试的单方面经验可能性方法。当$ n $和$ n $和$ p $都倾向于无限时，我们单方面的经验可能测试统计量的限制分布被证明为$ z^2i（z> 0）$。为了提高经验可能性测试统计统计的功能，我们还引入了重新验证的经验可能性测试统计统计。我们进行了一项广泛的仿真研究，以比较重新固定的经验可能性方法的性能和其他两个与平方样品相关系数总和有关的统计数据。
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.
