Abstract
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.
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Cena, A., Pistone, G. Exponential statistical manifold. AISM 59, 27–56 (2007). https://doi.org/10.1007/s10463-006-0096-y
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DOI: https://doi.org/10.1007/s10463-006-0096-y