The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics
An algorithm is proposed for exact computation of p-values for rank tests in the case where all possible realizations, e.g., rank permutations, have the same probability under \(H_0\). The algorithm is based on the splitting of the probability generating function into a product of two functions and symbolic calculation of coefficients in the power expansions of these functions. (\textit{Mathematica} software is used in the example calculations). It is described how to use this algorithm for signed rank tests, two sample rank tests, rank tests for simple regression models and rank autocorrelation tests. The algorithm can be used for tied ranks and censored data.
scientific article; zbMATH DE number 1878628