A Large Deviation-Type Approximation for the “Box Class” of Likelihood Ratio Criteria

Abstract

For a large class of tests related to the multivariate normal distribution a number of approximations to the distribution of the log-likelihood ratio statistic are discussed. Some of the approximations require the use of a small personal computer for their calculation, but this pays off in terms of giving very accurate approximations. Actually, one of the approximations, based on the use of a conjugate distribution, works well for all sample sizes and all significance levels.