Given a sequence of ϕ-mixing random variables not necessarily stationary, a Chernoff-Savage theorem for two-sample linear rank statistics is proved using the Pyke-Shorack  approach based on weak convergence properties of empirical processes in an extended metric. This result is a generalization of Fears and Mehra  in that the stationarity is not required and that the condition imposed on the mixing numbers is substantially relaxed. A similar result is shown to hold for strong mixing sequences under slightly stronger conditions on the mixing numbers.
AMS 1970 Subject Classifications
Primary 60F05, 62E20 Secondary 62G10
Key words and phrases
ϕ-mixing process two-sample linear rank statistics weak convergence of empirical processes
This is a preview of subscription content, log in to check access.
Yoshihara, K. (1974). Extension of Billingsley's theorems on weak convergence of empirical processes,Zeit. Wahrscheinlichkeitsth.,29, 87–92.MathSciNetCrossRefGoogle Scholar
Yoshihara, K. (1976). Weak convergence of multidimensional empirical processes for strong mixing sequences of stochastic vectors,Zeit. Wahrscheinlichkeitsth.,33, 133–137.MathSciNetCrossRefGoogle Scholar