Euclidean geometry of curved exponential families and its application to confidence regions

Abstract

Efron and Amari presented a Riemannian geometric framework for curved exponential families and studied the information loss and the variance of the estimate using this framework. In this paper, we propose a relatively simple geometric framework in Euclidean space. Based on this new framework, we study confidence regions for curved exponential families which have not been studied by Efron and Amari. The results obtained by Hamilton et al. are extended to curved exponential families.