Optical local Gaussian approximation of an exponential family - Mammen, Enno (Probability theory and related fields, 1987)
Summary Under certain regularity conditions products En of an experiment E can be locally approximated by homoschedastic Gaussian experiments Gn. Gn can be defined such that the square roots of the densities have nearly the same structure with respect to the L2-geometry as in En. The main result of this paper is that this choice of Gn is asymptotically optimal in the sense of minimizing the deficiency distance between En and G if E is a one-dimensional exponential family.