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Biometrika 2005 92(1):173-182; doi:10.1093/biomet/92.1.173
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© 2005 Biometrika Trust

Power of edge exclusion tests in graphical Gaussian models

M. Fátima Salgueiro1, Peter W. F. Smith2 and John W. McDonald2

1 Departamento de Métodos Quantitativos, ISCTE Business School, Av. Forças Armadas, 1649-026 Lisboa, Portugal fatima.salgueiro{at}iscte.pt, 2 Southampton Statistical Sciences Research Institute, University of Southampton, Southampton SO17 1BJ, U.K. pws{at}socsci.soton.ac.uk, bigmac{at}socsci.soton.ac.uk

Asymptotic multivariate normal approximations to the joint distributions of edge exclusion test statistics for saturated graphical Gaussian models are derived. Non-signed and signed square-root versions of the likelihood ratio, Wald and score test statistics are considered. Noncentral chi-squared approximations are also considered for the non-signed versions. These approximations are used to estimate the power of edge exclusion tests and an example is presented.

Key Words: Likelihood ratio test; Overall power; Partial correlation; Score test; Signed square-root test; Wald test

Received February 2003. Revised June 2004.


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