The probability that the estimated between-group covariance matrix is not positive definite is computed exactly under certain conditions given in Hill and Thompson (1978) for the balanced single classification multi-vanate analysis of variance with random effects. The computation is done using the Pfaffian method. This method can also be used more generally to calculate the cummulative distribution function of the largest root of the matrixwhere S1and S2are independent central Wishart matrices with common covariance matrices. The Pfaffian method is found to be a rapid and highly practical alternative to an algorithm of Venables (1974).
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