A Normal Approximation for the Multivariate Likelihood Ratio Statistics

  • Govind S. Mudholkar
  • Madhusudan C. Trivedi
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)


For many multivariate hypotheses, under the normality assumptions, the likelihood ratio tests are optimal in the sense of having maximal exact slopes. The exact distributions needed for implementing these tests are complex and their tabulation is limited in scope and accessibility. In this paper, a method of constructing normal approximations to these distributions is described, and illustrated using the problems of testing sphericity and independence between two sets of variates. The normal approximations are compared with well-known competing approximations and are seen to fare well.

Key Words

Sphericity independence between two sets of variates 


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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Govind S. Mudholkar
    • 1
  • Madhusudan C. Trivedi
    • 2
  1. 1.Department of StatisticsUniversity of RochesterRochesterUSA
  2. 2.Pennwalt Corporation Pharmaceutical DivisionRochesterUSA

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