Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution
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.
Related
- Restricted Maximum Likelihood Estimation in Generalized Linear Mixed Models
- Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process
- A Sharp Signal-to-Noise Threshold for Quasi-Maximum Likelihood Breakpoint Estimation
- Unrestricted conditional maximum likelihood estimation for a Fréchet regression model
- Approximate maximum likelihood estimation for partially observed fractional diffusions from discrete observations
BibTeX
@misc{samaraweera2026maximum,
title = {{Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution}},
author = {Sharindi Amasha Samaraweera and Leif Ellingson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31503},
eprint = {2610.31503},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31503},
}
RIS
TY - UNPB
TI - Maximum Likelihood Estimation and Likelihood Ratio Tests for the Power Spherical Distribution
AU - Sharindi Amasha Samaraweera
AU - Leif Ellingson
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31503
UR - https://arxiv.org/abs/2610.31503
AB - 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.
ER -