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

TL;DR

This paper characterizes when the Fisher Information matrix becomes singular in sine-skewed distributions on the d-dimensional torus, highlighting implications for statistical inference in asymmetric toroidal data models.

Contribution

It provides a general characterization of sine-skewed models on the d-dimensional torus that exhibit Fisher information singularity, addressing an open question in the field.

Findings

Identifies conditions leading to Fisher information singularity.

Provides a comprehensive characterization in the d-dimensional setting.

Highlights implications for inference in skewed toroidal distributions.

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.