Near-exact distributions for the likelihood ratio statistic used to test the reality of a covariance matrix

2013 ◽  
Author(s):  
Luís M. Grilo ◽  
Carlos A. Coelho
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Exact Distributions

The Exact and Near-Exact Distributions of the Likelihood Ratio Statistic for the Block Sphericity Test

2010 ◽  
Author(s):  
Filipe J. Marques ◽  
Carlos A. Coelho ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Statistic ◽  
Sphericity Test ◽  
Exact Distributions

scholarly journals Near-Exact Distributions for Likelihood Ratio Statistics Used in the Simultaneous Test of Conditions on Mean Vectors and Patterns of Covariance Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-25 ◽  
Author(s):  
Carlos A. Coelho ◽  
Filipe J. Marques ◽  
Sandra Oliveira
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Exact Distribution ◽  
Covariance Matrices ◽  
Distribution Functions ◽  
Small Samples ◽  
Chi Square ◽  
Exact Distributions ◽  
Mean Vectors ◽  
Likelihood Ratio Statistics

The authors address likelihood ratio statistics used to test simultaneously conditions on mean vectors and patterns on covariance matrices. Tests for conditions on mean vectors, assuming or not a given structure for the covariance matrix, are quite common, since they may be easily implemented. But, on the other hand, the practical use of simultaneous tests for conditions on the mean vectors and a given pattern for the covariance matrix is usually hindered by the nonmanageability of the expressions for their exact distribution functions. The authors show the importance of being able to adequately factorize the c.f. of the logarithm of likelihood ratio statistics in order to obtain sharp and highly manageable near-exact distributions, or even the exact distribution in a highly manageable form. The tests considered are the simultaneous tests of equality or nullity of means and circularity, compound symmetry, or sphericity of the covariance matrix. Numerical studies show the high accuracy of the near-exact distributions and their adequacy for cases with very small samples and/or large number of variables. The exact and near-exact quantiles computed show how the common chi-square asymptotic approximation is highly inadequate for situations with small samples or large number of variables.

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