Saddlepoint approximations for the probability mass functions of some nonparametric test statistics

Abstract

We give classical saddlepoint approximations for the probability mass functions of two nonparametric test statistics, the Kendall’s tau coefficient and the Wilcoxon signed-rank statistic. Then, we provide numerical comparisons, by comparing the exact probabilities with the saddlepoint approximation, a large deviation local limit theorem, an Edgeworth expansion and a normal approximation.