On the Tightness of the Laplace Approximation for Statistical Inference

Published 17 Oct 2022 in math.ST and stat.TH | (2210.09442v2)

Abstract: Laplace's method is used to approximate intractable integrals in a statistical problems. The relative error rate of the approximation is not worse than $O_p(n^{-1})$. We provide the first statistical lower bounds showing that the $n^{-1}$ rate is tight.

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