On Obtaining Permutation Distributions in Polynomial Time
提出了多项式时间算法，用于计算任何线性组合统计量的置换分布，涵盖Fisher两样本位置统计量及Wilcoxon等常见非参数统计量，并扩展到多样本和单样本情形，处理分层、结和删失数据。
Abstract Polynomial time algorithms are presented for finding the permutation distribution of any statistic that is a linear combination of some function of either the original observations or the ranks. This class of statistics includes the original Fisher two-sample location statistic and such common nonparametric statistics as the Wilcoxon, Ansari-Bradley, Savage, and many others. The algorithms are presented for the two-sample problem and it is shown how to extend them to the multisample problem—for example, to find the distribution of the Kruskal-Wallis and other extensions of the Wilcoxon—and to the single-sample situation. Stratification, ties, and censored observations are also easily handled by the algorithms. The algorithms require polynomial time as opposed to complete enumeration algorithms, which require exponential time. This savings is effected by first calculating and then inverting the characteristic function of the statistic.