arXiv subjects

Clara Bertinelli Salucci

Publications and source records attributed to Clara Bertinelli Salucci.

4 recordsLinked to original sources

arXiv2026

Asymptotic distribution of the likelihood ratio test statistic with inequality-constrained nuisance parameters

The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated tangent cone, unifying a wide range of previously isolated special cases. While the weights are fully understood for an arbitrary number of parameters of interest on the boundary, much less is known when nuisance parameters are also constrained to the boundary, a situation that frequently arises in applications. We provide the first general characterization of the asymptotic distribution of the likelihood-ratio test statistic when both the number of parameters of interest and the number of nuisance parameters on the boundary are arbitrary. We analyze how the cone geometry changes when moving from a problem with K parameters of interest on the boundary to one with K-m parameters of interest and m nuisances. In the orthogonal case we show that the resulting change in the chi-bar weights admits a closed-form difference pattern that redistributes probability mass across adjacent degrees of freedom, and that this pattern remains the dominant component of the weight shift under arbitrary covariance structures when the nuisance vector is one-dimensional. For a generic number of nuisance parameters, we introduce a new rank-based aggregation of intrinsic volumes that yields an accurate approximation of the mixture weights. Comprehensive simulations support the theory and demonstrate the accuracy of the proposed approximation.

stat.ME↗

arXiv2025

The asymptotic distribution of the likelihood ratio test statistic in two-peak discovery experiments

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.

hep-ex↗

arXiv2025

A note on the asymptotic distribution of the Likelihood Ratio Test statistic under boundary conditions

In the context of likelihood ratio testing with parameters on the boundary, we revisit two situations for which there are some discrepancies in the literature: the case of two parameters of interest on the boundary, with all other parameters in the interior, and the case where one of the two parameters on the boundary is a nuisance parameter. For the former case, we clarify that two seemingly conflicting results are consistent upon closer examination. For the latter, we clarify the source of the discrepancy and explain the different findings. As for this case the closed-form expression is valid only under positive correlation, we further propose a heuristic modification to the asymptotic distribution of the likelihood ratio test that extends its applicability to cases involving negative correlation.

math.ST↗

arXiv2021

Multivariable Fractional Polynomials for lithium-ion batteries degradation models under dynamic conditions

Longevity and safety of lithium-ion batteries are facilitated by efficient monitoring and adjustment of the battery operating conditions. Hence, it is crucial to implement fast and accurate algorithms for State of Health (SoH) monitoring on the Battery Management System. The task is challenging due to the complexity and multitude of the factors contributing to the battery degradation, especially because the different degradation processes occur at various timescales and their interactions play an important role. Data-driven methods bypass this issue by approximating the complex processes with statistical or machine learning models. This paper proposes a data-driven approach which is understudied in the context of battery degradation, despite its simplicity and ease of computation: the Multivariable Fractional Polynomial (MFP) regression. Models are trained from historical data of one exhausted cell and used to predict the SoH of other cells. The data are characterised by varying loads simulating dynamic operating conditions. Two hypothetical scenarios are considered: one assumes that a recent capacity measurement is known, the other is based only on the nominal capacity. It was shown that the degradation behaviour of the batteries under examination is influenced by their historical data, as supported by the low prediction errors achieved (root mean squared errors from 1.2% to 7.22% when considering data up to the battery End of Life). Moreover, we offer a multi-factor perspective where the degree of impact of each different factor is analysed. Finally, we compare with a Long Short-Term Memory Neural Network and other works from the literature on the same dataset. We conclude that the MFP regression is effective and competitive with contemporary works, and provides several additional advantages e.g. in terms of interpretability, generalisability, and implementability.

stat.AP↗