# Fisher Information and Exponential Families Parametrized by a Segment of Means

Abstract : We consider natural and general exponential families $(Q_m)_{m\in M}$ on $\mathbb{R}^d$ parametrized by the means. We study the submodels $(Q_{\theta m_1+(1-\theta)m_2})_{\theta\in[0,1]}$ parametrized by a segment in the means domain, mainly from the point of view of the Fisher information. Such a parametrization allows for a parsimonious model and is particularly useful in practical situations when hesitating between two parameters $m_1$ and $m_2$. The most interesting examples are obtained when $\mathbb{R}^d$ is a linear space of matrices, in particular for Gaussian and Wishart models.
Domain :

Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00942218
Contributor : Piotr Graczyk <>
Submitted on : Thursday, February 6, 2014 - 8:54:20 AM
Last modification on : Monday, March 9, 2020 - 6:15:59 PM
Document(s) archivé(s) le : Tuesday, May 6, 2014 - 10:07:08 PM

### Files

Graczyk_Mamane.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00942218, version 1
• ARXIV : 1402.1305

### Citation

Piotr Graczyk, Salha Mamane. Fisher Information and Exponential Families Parametrized by a Segment of Means. 2014. ⟨hal-00942218⟩

Record views