Asymptotic distribution of simple linear rank statistics for testing symmetry

Abstract

The object of the present paper is to derive asymptotic distributions of simple linear rank statistics used for testing symmetry under various systems of conditions. The main result is stated in Theorem 3 (Section 2) and in Theorem 6 (Section 3). The assertions have been derived by the method worked out in [1]. Similar assertions concerning the multivariate case (the other part of the author's thesis) will be published in a next paper.