On the consistency of a two-sample matching test

Abstract

Let {X k} and {Y k}, 1 ≤ k ≤n be the order statistics of independent random samples from continuous distribution function F and G respectively. To test the null hypothesis H 0 : G = F, known, against the alternative H 1 : G ≠ F, a test S n, based on the number of matches between the two samples was suggested by Siddiqui and Gürler (1992). In this note the asymptotic distribution of S n under the null hypothesis is obtained and its consistency against a fixed alternative is shown.