On parameter estimation for $N(μ,σ^2 I_3)$ based on projected data into $\mathbb{S}^2$
Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari
公開日: 2024/10/29
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.