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Exact test theory in Gaussian graphical models
Örebro University, Örebro University School of Business. Unit of Statistics.ORCID iD: 0000-0003-1359-3311
Department of Mathematics, Stockholm University, Stockholm, Sweden.
2023 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 196, article id 105185Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 196, article id 105185
Keywords [en]
Gaussian graphical model, Precision matrix, Test theory
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-106070DOI: 10.1016/j.jmva.2023.105185ISI: 000976976000001Scopus ID: 2-s2.0-85151516814OAI: oai:DiVA.org:oru-106070DiVA, id: diva2:1759581
Funder
Örebro UniversityAvailable from: 2023-05-26 Created: 2023-05-26 Last updated: 2023-05-26Bibliographically approved

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Bodnar, Olha

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