THE LIMITING NORMALITY OF THE TEST STATISTIC FOR THE TWO-SAMPLE PROBLEM INDUCED BY A CONVEX SUM DISTANCE

KAORU FUEDA

Graduate School of Mathematics, Kyushu University, Higashi-ku, Hakozaki 6-10-1, Fukuoka 812, Japan

(Received October 14, 1991; revised September 13, 1995)

Abstract. Critchlow (1992, J. Statist. Plann. Inference, 32, 325–346) proposed a method of a unified construction of a class of rank tests. In this paper, we introduce a convex sum distance and prove the limiting normality of the test statistics for the two-sample problem derived by his method.

Key words and phrases: Convex sum distance, transposition property, limiting normality.