On the chernoff-savage theorem for dependent sequences

Abstract

SummaryGiven a sequence of c-mixing random variables not necessarily stationary, a Chernoff-Savage theorem for two-sample linear rank statistics is proved using the Pyke-Shorack [5] approach based on weak convergence properties of empirical processes in an extended metric. This result is a generalization of Fears and Mehra [4] 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.

Some Contributions to Chernoff-Savage Theorems

“…Hence one can proceed as in Theorem 5 if condition (Eg) is satisfied (then Proposition 2 can be applied). But for p Theorem 6 extends the results for the Chernoff-Savage theorem in the uniformly mixing case, especially those ofFears, Mehra (1974) andAhmad, Lin (1980). In the latter paper the mixing rate…”

“…Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 6/11/15 7:50 AM Ahmad, Lin (1980), Fears, Mehra (1974), and Mehra, Rao (1975, 1978 first establish a weak convergence result of scme weighted two sample empirical process as in Pyke, Shorack (1968 Here we have to use the following basic inequality (Davydov (1970)):…”

“…For strongly mixing processes a Chernoff-Savage theorem is contained in Ahmad and Lin (1980). There the assumptions are cx(k) = and the class of functions h is contained in some ©ij, where 6,6'>0.…”