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SYNOPTIC ABSTRACT
Let λ* be the modified likelihood ratio criterion for testing the multisample sphericity hypothesis H: Σj = σ2I, j = 1, …, k, where Σj is the positive definite covariance matrix of the jth normal population. Asymptotic expansions for the distribution of λ* are derived, under two classes of local alternatives. The results are an extension of those in Khatri and Srivastava (1974) in multisample sphericity.
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