Scalable Monte Carlo Inference and Rescaled Local Asymptotic Normality
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Statisticians are usually glad to obtain additional data, but Monte Carlo inference can lead to an embarrassment of riches since the appealing generality of Monte Carlo methods can come at the expense of poor scalability. We consider statistically efficient simulation-based likelihood inference with a computational budget of size essentially n^3/2 for a dataset of size n. This methodology takes advantage of asymptotic properties of the likelihood function in an n^-1/4 neighborhood of the true parameter value. We obtain a rescaled version of local asymptotic normality, and on this scale we show that statistically efficient estimation is possible despite inconsistent Monte Carlo likelihood evaluation.
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