Scalable Monte Carlo Inference and Rescaled Local Asymptotic Normality
Statistics Theory
2020-12-02 v2 Probability
Methodology
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2007.00723,
title = {Scalable Monte Carlo Inference and Rescaled Local Asymptotic Normality},
author = {Ning Ning and Edward Ionides and Ya'acov Ritov},
journal= {arXiv preprint arXiv:2007.00723},
year = {2020}
}
Comments
41 pages, 1 figure