Near-exact distributions for the independence and sphericity likelihood ratio test statistics

Authors:
Carlos A. Coelho;Filipe J. Marques
Affiliations:
Mathematics Department, Faculty of Sciences and Technology, The New University of Lisbon, Portugal;Mathematics Department, Faculty of Sciences and Technology, The New University of Lisbon, Portugal
Venue:
Journal of Multivariate Analysis
Year:
2010

Citing 2
Cited 2

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The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables

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Asymptotic distributions of some test criteria for the mean vector with fewer observations than the dimension

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Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions

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Abstract

In this paper we show how, based on a decomposition of the likelihood ratio test for sphericity into two independent tests and a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates, we may obtain extremely well-fitting near-exact distributions for both test statistics. Since both test statistics have the distribution of the product of independent Beta random variables, it is possible to obtain near-exact distributions for both statistics in the form of Generalized Near-Integer Gamma distributions or mixtures of these distributions. For the independence test statistic, numerical studies and comparisons with asymptotic distributions proposed by other authors show the extremely high accuracy of the near-exact distributions developed as approximations to the exact distribution. Concerning the sphericity test statistic, comparisons with formerly developed near-exact distributions show the advantages of these new near-exact distributions.