Joint asymptotic multinormality for a class of rank order statistics in multivariate paired comparisons

The joint asymptotic multinormality of certain linear signed-rank statistics introduced by Shane and Puri (1969) is established for the nonidentically distributed case; moreover, the usual restriction forbidding constant score generating functions is dropped. In addition, sufficient conditions more general than those of Shane and Puri are given for the convergence of certain dispersion matrices, and these conditions guarantee the asymptotic independence of the statistics under consideration.