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arXiv · 2410.22384

On parameter estimation for $N(\mu,\sigma^2 I_3)$ based on projected data into $\mathbb{S}^2$

Jordi-Lluís Figueras·Aron Persson·Lauri Viitasaari
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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.

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Jordi-Lluís Figueras, Aron Persson, Lauri Viitasaari. 2024-10-29. On parameter estimation for $N(\mu,\sigma^2 I_3)$ based on projected data into $\mathbb{S}^2$. https://doi.org/10.15559/25-vmsta279

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