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.
Acknowledgements
The authors would like to thank the anonymous reviewers, the Associate Editor, and the Editor-in-Chief for their constructive comments that greatly improved the quality of this paper. This research project was supported by NSF grant DMS-1761603.
Citation
Ning Ning. Edward L. Ionides. Ya’acov Ritov. "Scalable Monte Carlo inference and rescaled local asymptotic normality." Bernoulli 27 (4) 2532 - 2555, November 2021. https://doi.org/10.3150/20-BEJ1321
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