The exact and near-exact distributions of the main likelihood ratio test statistics used in the complex multivariate normal setting

Carlos Coelho (), Barry Arnold () and Filipe Marques ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 2, 386-416

Abstract: In this paper the authors show how it is possible to establish a common structure for the exact distribution of the main likelihood ratio test (LRT) statistics used in the complex multivariate normal setting. In contrast to what happens when dealing with real random variables, for complex random variables it is shown that it is possible to obtain closed-form expressions for the exact distributions of the LRT statistics to test independence, equality of mean vectors and the equality of an expected value matrix to a given matrix. For the LRT statistics to test sphericity and the equality of covariance matrices, cases where the exact distribution has a non-manageable expression, easy to implement and very accurate near-exact distributions are developed. Numerical studies show how these near-exact distributions outperform by far any other available approximations. As an example of application of the results obtained, the authors develop a near-exact approximation for the distribution of the LRT statistic to test the equality of several complex normal distributions. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Covariance matrix; Equality of covariance matrices; Equality of mean vectors; Fourier transforms; Generalized integer gamma (GIG) distribution; Generalized near-integer gamma (GNIG) distribution; Independence; Mixtures; Expected value matrix; Sphericity; Statistical distributions (distribution functions); 62H05; 62H10; 62E15; 62H15; 62E20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11749-014-0418-y

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