Exponential statistical manifold
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- 作者：Alberto Cena and Giovanni Pistone
- 关键词：Information geometry ; Statistical manifold ; Orlicz space ; Moment generating functional ; Cumulant generating functional ; Kullback– ; Leibler divergence
- 刊名：Annals of the Institute of Statistical Mathematics
- 出版时间：March, 2007
- 出版年：2007
- 期刊代码：1_00203157
- 类别：et
- 卷：59
- 期：1
- 页码：27-56
- 数据来源：sp
摘要
We consider the non-parametric statistical model ε(p) of all positive densities q that are connected to a given positive density p by an open exponential arc, i.e. a one-parameter exponential model p(t), t ∈ I, where I is an open interval. On this model there exists a manifold structure modeled on Orlicz spaces, originally introduced in 1995 by Pistone and Sempi. Analytic properties of such a manifold are discussed. Especially, we discuss the regularity of mixture models under this geometry, as such models are related with the notion of e- and m-connections as discussed by Amari and Nagaoka.