Distribution of the likelihood ratio criterion for testing a hypothesis specifying a covariance matrix

Abstract

SUMMARY The exact null distribution of the likelihood ratio criterion for testing the null hypothesis Σ θ σ 0 against the alternative Σ ≠ Σ 0 in N p (μ, Σ) has been obtained in a series form and percentage points computed for p θ 2 (1) 10 for α θ 0.005, 0.01, 0.025, 0.05, 0.1 and 0.25 and various degrees of freedom, but only selected tables are presented here.