Directional testing for high dimensional multivariate normal distributions

Huang, Caizhu; Caterina, Claudia Di; Sartori, Nicola

doi:10.1214/22-ejs2089

Cited by 2 publications

(2 citation statements)

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“…When the re-normalized saddlepoint approximation is exact, then the directional test will also be exact, as the re-normalization is automatically incorporated in (2.10). McCormack et al (2019) established this exactness for a number of tests for multivariate normal models, and Huang, Di Caterina, and Sartori (2022) were able to prove exactness for the case of testing a saturated Gaussian graphical model in Davison et al (2014, Sect. 5.3).…”

Section: Directional Tests In Linear Exponential Familiesmentioning

confidence: 85%

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Directional Tests in Gaussian Graphical Models

Caterina¹,

Reid²,

Sartori³

2025

STAT SINICA

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Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and leads to exact control of the size of the tests, given that the only approximation error involved is due to the numerical calculation of two scalar integrals. Although exactness is not guaranteed for non-chordal graphs, the ability of the saddlepoint approximation to control the relative error leads the directional test to overperform its competitors even in these cases. The accuracy of our proposal is verified by simulation experiments under challenging scenarios, where inference via standard asymptotic approximations to the likelihood ratio test and some of its higher-order modifications fails. The directional approach is used to illustrate the assessment of Markovian dependencies in a dataset from a veterinary trial on cattle. A second example with microarray data shows how to select the graph structure related to genetic anomalies due to acute lymphocytic leukemia.

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Section: Directional Tests In Linear Exponential Familiesmentioning

confidence: 85%

“…A much simpler problem in covariance selection, limited to testing an incomplete graph versus the saturated model, was studied by Davison et al (2014, Sect. 5.3) and shown to be exact in Huang, Di Caterina, and Sartori (2022). Our extension involves both theoretical and computational innovations.…”

Section: Introductionmentioning

confidence: 95%