Asymptotic Multinormality and Remainder Terms D D Cof Linear Rank Vectors Under Alternatives

Asymptotic multinormality of linear rank statistics based on independent vector valued random variables is obtained. Under suitable assumptions, weak esti-mates for the remainder terms for convergence to normality are also obtained. Results on asymptotic normality are re-lated to Ha’j ek (1968) and Pun and Sen ( 1969). Re— suits on the remainder terms are related to those ofJure~kov ~ and Pun ( 1975), Bergstrom and Pun ( 1977) , andHu~kov ~ (1977)