A variety of exponential models with affine dual foliations have been noted to possess certain rather similar statistical properties. To give a precise meaning to what has been conceived as "similar," we here propose a set of five conditions, of a differential geometric/statistical nature, that specify the class of what we term orthogeodesic models. It is discussed how these conditions capture the properties in question, and it is shown that some important nonexponential models turn out to satisfy the conditions, too. The conditions imply, in particular, a higher-order asymptotic independence result. A complete characterization of the structure of exponential orthogeodesic models is derived.
"Orthogeodesic Models." Ann. Statist. 21 (2) 1018 - 1039, June, 1993. https://doi.org/10.1214/aos/1176349162