Geometrical foundations of asymptotic inference are described in simple cases, without the machinery of differential geometry. A primary statistical goal is to provide a deeper understanding of the ideas of Fisher and Jeffreys. The role of differential geometry in generalizing results is indicated, further applications are mentioned, and geometrical methods in nonlinear regression are related to those developed for general parametric families.
"The Geometry of Asymptotic Inference." Statist. Sci. 4 (3) 188 - 219, August, 1989. https://doi.org/10.1214/ss/1177012480