The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments
- 1University of Oslo
Abstract
Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks’ theorem. This assumption breaks down when parameters such as signal or coupling strengths are restricted to be non-negative and their values under the null hypothesis lie on the boundary of the parameter space. Based on a recent clarification concerning the correct asymptotic distribution of the likelihood ratio test statistic for cases where two of the parameters are on the boundary, we revisit the the question of significance estimation for two-peak signal-plus-background counting experiments. In the high-energy physics literature, such experiments are commonly analyzed using Wilks’ chi-squared distribution or the one-parameter Chernoff limit. We demonstrate that these approaches can lead to strongly miscalibrated significances, and that the test statistic distribution is instead well described by a chi-squared mixture with weights determined by the Fisher information matrix. Our results highlight the need for boundary-aware asymptotics in the analysis of two-peak counting experiments.
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BibTeX
@article{salucci2026asymptotic,
title = {{The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments}},
author = {Clara Bertinelli Salucci and Hedvig Borgen Reiersrud and A. L. Read and Anders Kvellestad and Riccardo De Bin},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16439-9},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16439-9},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments
AU - Clara Bertinelli Salucci
AU - Hedvig Borgen Reiersrud
AU - A. L. Read
AU - Anders Kvellestad
AU - Riccardo De Bin
PY - 2026
DA - 2026/10/21
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16439-9
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16439-9
AB - Likelihood ratio tests are widely used in high-energy physics, where the test statistic is usually assumed to follow a chi-squared distribution with a number of degrees of freedom specified by Wilks’ theorem. This assumption breaks down when parameters such as signal or coupling strengths are restricted to be non-negative and their values under the null hypothesis lie on the boundary of the parameter space. Based on a recent clarification concerning the correct asymptotic distribution of the likelihood ratio test statistic for cases where two of the parameters are on the boundary, we revisit the the question of significance estimation for two-peak signal-plus-background counting experiments. In the high-energy physics literature, such experiments are commonly analyzed using Wilks’ chi-squared distribution or the one-parameter Chernoff limit. We demonstrate that these approaches can lead to strongly miscalibrated significances, and that the test statistic distribution is instead well described by a chi-squared mixture with weights determined by the Fisher information matrix. Our results highlight the need for boundary-aware asymptotics in the analysis of two-peak counting experiments.
SN - 1434-6044
SN - 1434-6052
ER -