基于皮尔逊相关系数和其他统计检验的排列检验p值的快速计算
Fast computation of p-values for the permutation test based on Pearson's correlation coefficient and other statistical tests
摘要：
排列测试是最简单和最广泛使用的统计工具之一。它们的p值可以通过简单的排列采样来计算。然而，这种计算p值的方法通常非常慢，以至于它被近似值所取代，近似值仅对部分有趣的参数范围是准确的。此外，近似的精度通常不能通过增加计算时间来提高。我们介绍了一种新的基于抽样的算法，它使用快速傅立叶变换来计算p值的排列测试的基础上皮尔逊的相关系数。该算法实际上是渐近快于直接采样。通常，它的复杂度是输入大小的对数，而直接采样的复杂度是线性的。该算法背后的思想也可以用于加速许多其他常见统计测试的p值计算。该算法易于实现，但其分析涉及对称群表示理论的结果。
英文摘要：
Permutation tests are among the simplest and most widely used statistical tools. Their p-values can be computed by a straightforward sampling of permutations. However, this way of computing p-values is often so slow that it is replaced by an approximation, which is accurate only for part of the interesting range of parameters. Moreover, the accuracy of the approximation can usually not be improved by increasing the computation time. We introduce a new sampling-based algorithm which uses the fast Fourier transform to compute p-values for the permutation test based on Pearson's correlation coefficient. The algorithm is practically and asymptotically faster than straightforward sampling. Typically, its complexity is logarithmic in the input size, while the complexity of straightforward sampling is linear. The idea behind the algorithm can also be used to accelerate the computation of p-values for many other common statistical tests. The algorithm is easy to implement, but its analysis involves results from the representation theory of the symmetric group.
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