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2019 Hypothesis testing near singularities and boundaries
Jonathan D. Mitchell, Elizabeth S. Allman, John A. Rhodes
Electron. J. Statist. 13(1): 2150-2193 (2019). DOI: 10.1214/19-EJS1576


The likelihood ratio statistic, with its asymptotic $\chi ^{2}$ distribution at regular model points, is often used for hypothesis testing. However, the asymptotic distribution can differ at model singularities and boundaries, suggesting the use of a $\chi ^{2}$ might be problematic nearby. Indeed, its poor behavior for testing near singularities and boundaries is apparent in simulations, and can lead to conservative or anti-conservative tests. Here we develop a new distribution designed for use in hypothesis testing near singularities and boundaries, which asymptotically agrees with that of the likelihood ratio statistic. For two example trinomial models, arising in the context of inference of evolutionary trees, we show the new distributions outperform a $\chi ^{2}$.

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When this article was first made public, on June 28, 2019, its page numbering was incorrect (pp. 1250–1293). The article’s page numbers were corrected to 2150–2193 on July 30, 2019.


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Jonathan D. Mitchell. Elizabeth S. Allman. John A. Rhodes. "Hypothesis testing near singularities and boundaries." Electron. J. Statist. 13 (1) 2150 - 2193, 2019.


Received: 1 June 2018; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07089017
MathSciNet: MR3980955
Digital Object Identifier: 10.1214/19-EJS1576

Primary: 62E17
Secondary: 92D15


Vol.13 • No. 1 • 2019
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