A directional look at <i>F</i>‐tests

McCormack, Andrew; Reid, N.; Sartori, Nicola; Theivendran, Sri-Amirthan

doi:10.1002/cjs.11515

Cited by 3 publications

(3 citation statements)

References 5 publications

(20 reference 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%

“…Still, in those settings the directional test proved to be uniformly more powerful than the likelihood ratio test and its modifications considered here. It is also noteworthy that for simpler testing problems in the multivariate normal model, McCormack et al (2019) showed that the directional test is equivalent to the uniformly most powerful invariant test based on the F statistic or Hotelling's T 2 statistic.…”

Section: Discussionmentioning

confidence: 99%

“…The procedure was extended from linear exponential families to nonlinear parameters of interest in general continuous models by Fraser, Reid, and Sartori (2016). Besides its accuracy, the directional approach was found to coincide with exact results in several classical situations (McCormack et al (2019)).…”

Section: Introductionmentioning

confidence: 86%

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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%

Section: Discussionmentioning

confidence: 99%

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Directional Tests in Gaussian Graphical Models

Caterina¹,

Reid²,

Sartori³

2025

STAT SINICA

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D. A. S. Fraser: From structural inference to asymptotics

Reid

2022

Can J Statistics

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Directional testing for high-dimensional multivariate normal distributions

Huang

Caterina

Sartori

2021

Preprint

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Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components p is of the same asymptotic order as the sample size n, standard inferential techniques are generally inadequate to conduct hypothesis testing on the mean vector and/or the covariance matrix. Within several prominent frameworks, we propose then to draw reliable conclusions via a directional test. We show that under the null hypothesis the directional pvalue is exactly uniformly distributed even when p is of the same order of n, provided that conditions for the existence of the maximum likelihood estimate for the normal model are satisfied. Extensive simulation results confirm the theoretical findings across different values of p/n, and show that the proposed approach outperforms not only the usual finite-p approaches but also alternative methods tailored for high-dimensional settings.

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A directional look at F‐tests

Cited by 3 publications

References 5 publications

Directional Tests in Gaussian Graphical Models

Directional Tests in Gaussian Graphical Models

D. A. S. Fraser: From structural inference to asymptotics

Directional testing for high-dimensional multivariate normal distributions

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