Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution
Year: 2026
Type: preprint
Abstract: The Power Spherical distribution has been proposed as a computationally efficient alternative to the von Mises-Fisher distribution for data on the unit sphere, with reduced computational cost for simulation and a simpler normalizing constant. Despite these advantages, its statistical inference properties remain underdeveloped. In this paper, we develop a likelihood-based framework for estimation and inference for the Power Spherical distribution. Within this framework, we develop maximum likelihood estimation procedures for both the central direction and concentration parameter. Building on these estimators, we formulate likelihood ratio tests for hypotheses involving known and unknown parameters, study their asymptotic behavior, and evaluate finite-sample performance through simulation studies. The results demonstrate accurate Type I error control and good power when the asymptotic chi-square approximation is appropriate, while the parametric bootstrap provides reliable inference in small-sample settings or those where the dimension is large relative to the sample size. The findings also highlight nontrivial dependence of the power of tests for the central direction on the concentration parameter.
Source: arXiv (Cornell University)
Institution: Texas Tech University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223352243