Scalable Monte Carlo inference and rescaled local asymptotic normality

In this paper, we generalize the property of local asymptotic normality (LAN) to an enlarged neighborhood, under name rescaled (RLAN). We obtain sufficient conditions for a regular parametric model satisfy RLAN. show that RLAN supports construction statistically efficient estimator which maximizes cubic approximation log-likelihood on neighborhood. context Monte Carlo inference, find maximum likelihood can maintain its statistical efficiency in presence asymptotically increasing error evaluation.