Approximate Empirical Distributions for the Computation of Nonparametric Statistics

摘要

This paper discusses a method of approximating the value of a statistic through the use of a grouped frequency distribution. This is of particular interest for nonparametric statistics based on ranks, on the empirical distribution function or on order statistics since it avoids the process of ordering the data and can be carried out quickly, even for large sample sizes. Bounds on the error of approximation are obtained. When a natural grouping of the data exists, the approximation would be the proper statistic to use in its own right. The Wilcoxon signed-rank statistic is treated in detail and other statistics are considered. An efficient computational algorithm is presented. (Author)