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On the Tightness of the Laplace Approximation for Statistical Inference (2210.09442v2)
Published 17 Oct 2022 in math.ST and stat.TH
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.