Exact test theory in Gaussian graphical models

In this paper, we derive several statistical tests on the precision matrix with application to the determination of the structure of an undirected Gaussian graph. The exact distributions of the test statistics are obtained under the null hypotheses, while the exact distributions of the random matric...

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Bibliographic Details
Published in:Journal of multivariate analysis 2023-07, Vol.196, p.105185, Article 105185
Main Authors: Bodnar, Olha, Touli, Elena Farahbakhsh
Format: Article
Language:English
Subjects:
Gaussian graphical model
Precision matrix
Test theory
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Summary:In this paper, we derive several statistical tests on the precision matrix with application to the determination of the structure of an undirected Gaussian graph. The exact distributions of the test statistics are obtained under the null hypotheses, while the exact distributions of the random matrices, which are used in the construction of the test statistics, are deduced under the alternative hypothesis. Moreover, we present the high-dimensional asymptotic distributions of the test statistics under the null hypothesis. The testing problems that an undirected Gaussian graph possesses a structure that corresponds to the precision matrix of an AR(1) process, to the block-diagonal precision matrix and to the precision of a factor model are discussed in detail. The performance of the proposed statistical tests is further investigated via an extensive simulation study and compared to the benchmark approach.
ISSN:0047-259X
1095-7243
1095-7243
DOI:10.1016/j.jmva.2023.105185