论文标题
分析公式的衍生公式用于样品相关的样品矩与数据排列
Derivation of Analytic Formulas for the Sample Moments of the Sample Correlation over Permutations of Data
论文作者
论文摘要
皮尔逊的相关性是最广泛报道的关联措施之一。线性关联的统计证据的强度由假设检验的p值确定。如果数据集的真实分布是双变量正常的，则在特定的数据转换下，t统计量将返回确切的p值，否则是近似值。或者，可以通过分析数据排列下样品相关性的分布来估算p值。该分布的力矩近似未被广泛使用，因为对矩本身的估计在数值上是密集的，并且不确定性更大。在本文中，我们得出了一个电感公式，允许根据数据的中心矩来分析样品相关样品相关的样品矩。将这些公式放置在适当的统计框架中可以打开用于计算P值的新估计方法的可能性。
Pearson's correlation is among the mostly widely reported measures of association. The strength of the statistical evidence for linear association is determined by the p-value of a hypothesis test. If the true distribution of a dataset is bivariate normal, then under specific data transformations a t-statistic returns the exact p-value, otherwise it is an approximation. Alternatively, the p-value can be estimated by analyzing the distribution of the sample correlation under permutations of the data. Moment approximations of this distribution are not as widely used since estimation of the moments themselves are numerically intensive with greater uncertainties. In this paper we derive an inductive formula allowing for the analytic expression of the sample moments of the sample correlation under permutations of the data in terms of the central moments of the data. These formulas placed in a proper statistical framework could open up the possibility of new estimation methods for computing the p-value.
