Local asymptotic normality

Summary

A sequence of statistical models is locally asymptotically normal (LAN) at a parameter value if its log-likelihood ratios have a special form at scale $1/\sqrt{n}$. At that scale they look like those of a single observation from a normal location model. The notion is due to Lucien Le Cam. Smooth i.i.d. parametric models are LAN, with the Fisher information as the covariance. LAN is the setting of the asymptotic optimality theory of estimators and tests: the convolution theorem and the local asymptotic minimax theorem.