On parameter estimation for $N(\mu,\sigma^2 I_3)$ based on projected data into $\mathbb{S}^2$
Statistics Theory
2025-09-30 v1 Probability
Statistics Theory
Abstract
We consider the projected normal distribution, with isotropic variance, on the 2-sphere using intrinsic statistics. We show that in this case, the expectation commutes with the projection and that the covariance of the normal variable has a 1-1 correspondence with the intrinsic covariance of the projected normal distribution. This allows to estimate, after model identification, the parameters of the underlying normal distribution that generates the data.
Keywords
Cite
@article{arxiv.2410.22384,
title = {On parameter estimation for $N(\mu,\sigma^2 I_3)$ based on projected data into $\mathbb{S}^2$},
author = {Jordi-Lluís Figueras and Aron Persson and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2410.22384},
year = {2025}
}