Sur l'approximation de familles de mesures par des familles gaussiennes
The local asymptotic theory is often based upon the approximation of a family of measures corresponding to a (not necessarily parametric) model by a Gaussian family. Almost minimal conditions are given to imply the approximability for various distances between experiments, without definitely solving the problem for the strong distance. This long paper didactically presents this theoretical question. It gives general conditions, weaker than the usual LAN ones, and situates the other local asymptotic frameworks. It shows that a Lindeberg condition on square roots of densities is necessary and sufficient in the case of independent, identically distributed variables, and extends results in the case of observations neither independent nor identically distributed, with extra assumptions of asymptotic negligibility of conditional information. Some applications will be provided in a future work.
local approximations of families of measures
non independent, non identically distributed observations
Lindeberg condition on square roots of densities
asymptotic negligibility of conditional information
scientific article; zbMATH DE number 3936183