Abstract: Applying the strong approximation technique we present a unified approach to asymptotic results for multivariate linear rank statistics for the two-sample problem. We reprove asymptotic normality of these statistics under the null hypothesis and under local alternatives convergent at a moderate rate to the null hypothesis. We also provide a moderate deviation theorem for these statistics under the null hypothesis. Proofs are short and use natural argumentation.

2000 AMS Mathematics Subject Classification: Primary: 62E20; Secondary: 62G20, 60F15, 60F05, 60F10.

Keywords and phrases: Two-sample problem, linear rank statistics, Hungarian construction, moderate deviations, local alternatives, asymptotic distribution, asymptotic normality.