On parameter estimation for $N(μ,σ^2 I_3)$ based on projected data into $\mathbb{S}^2$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911182997159936 |
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| author | Figueras, Jordi-Lluís Persson, Aron Viitasaari, Lauri |
| author_facet | Figueras, Jordi-Lluís Persson, Aron Viitasaari, Lauri |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On parameter estimation for $N(μ,σ^2 I_3)$ based on projected data into $\mathbb{S}^2$ Figueras, Jordi-Lluís Persson, Aron Viitasaari, Lauri Statistics Theory Probability 62H11, 62F10 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. |
| title | On parameter estimation for $N(μ,σ^2 I_3)$ based on projected data into $\mathbb{S}^2$ |
| topic | Statistics Theory Probability 62H11, 62F10 |
| url | https://arxiv.org/abs/2410.22384 |