Scalable Monte Carlo Inference and Rescaled Local Asymptotic Normality

TL;DR

This paper extends local asymptotic normality to larger neighborhoods, enabling efficient Monte Carlo inference even with increasing likelihood estimation errors, by introducing rescaled local asymptotic normality (RLAN).

Contribution

It introduces RLAN, a generalization of LAN, providing conditions for its applicability and demonstrating its use for efficient Monte Carlo inference with increasing likelihood errors.

Findings

RLAN extends LAN to larger neighborhoods.

Efficient estimators can be constructed under RLAN.

Monte Carlo estimators retain efficiency despite increasing errors.

Abstract

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