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arXiv · 2207.13954

Beyond the delta method

Antoine Lejay·Sara Mazzonetto
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Abstract

We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is explicitly computable, gives some insights about the non-asymptotic behavior of the renormalized MLE and its departure from its limit. We highlight that the results hold whenever the score and its derivative converge, including to non Gaussian limits. Our approach is based on an asymptotic implicit function theorem, inspired from perturbative approaches.

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Antoine Lejay, Sara Mazzonetto. 2022-07-28. Beyond the delta method. https://arxiv.org/abs/2207.13954

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