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arXiv · 2603.04369

On the singularity of the Fisher Information matrix in the sine-skewed family on the d-dimensional torus

Emily Schutte·Sophia Loizidou·Vincent Laheurte
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Abstract

Skewed distributions are fundamental in modelling asymmetric data on the d-dimensional torus. In this context, asymmetry is introduced through the sine-skewing mechanism, which is the only skewing mechanism that has been proposed on the hyper-torus in the literature. Some sine-skewed models are known to suffer from a singular Fisher information matrix in the vicinity of symmetry, which poses a significant issue for inferential purposes. It is an open question to determine for which sine-skewed models Fisher information singularity occurs. In this paper, a general characterization of the class of models that exhibit this singularity is given in the general d-dimensional setting.

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Emily Schutte, Sophia Loizidou, Vincent Laheurte. 2026-03-04. On the singularity of the Fisher Information matrix in the sine-skewed family on the d-dimensional torus. https://arxiv.org/abs/2603.04369

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