A General Class of One-Sample Nonparametric Test Statistics Based on Subsamples

A general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations. The test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m = 1 and a modified Wilcoxon signed-rank test statistic for m = 2. Asymptotic normality of properly standardized versions of our statistics is established under general conditions. Small sample power simulations as well as Pitman and Bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics.