 Local asymptotic normality

A regular statistical model is locally asymptotically normal at ${\theta }_0$ when its log-likelihood ratio under local shifts ${\theta }_0+h/\sqrt{n}$ has the expansion

Local asymptotic normality (LAN) is a concept used in the field of statistics and estimation theory, particularly in the context of statistical inference and asymptotic theory. It provides a framework to analyze the behavior of maximum likelihood estimators (MLEs) and similar statistical procedures in large samples.