On the consistency of a two-sample matching test
Ülkü Gürler, M. M. Siddiqui · Journal of nonparametric statistics · 1996
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.