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On the tightness of the Laplace approximation for statistical inference

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  • Bilodeau, Blair
  • Tang, Yanbo
  • Stringer, Alex

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 Op(n−1). We provide the first statistical lower bounds showing that the n−1 rate is tight.

Suggested Citation

  • Bilodeau, Blair & Tang, Yanbo & Stringer, Alex, 2023. "On the tightness of the Laplace approximation for statistical inference," Statistics & Probability Letters, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:stapro:v:198:y:2023:i:c:s0167715223000639
    DOI: 10.1016/j.spl.2023.109839
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    References listed on IDEAS

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    1. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
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