On the chernoff-savage theorem for dependent sequences

  • Ibrahim A. Ahmad
  • Pi-Erh Lin


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 [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.

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 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1980

Authors and Affiliations

  • Ibrahim A. Ahmad
    • 1
    • 2
  • Pi-Erh Lin
    • 1
    • 2
  1. 1.Memphis State UniversityUSA
  2. 2.Florida State UniversityUSA

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