Beyond the delta method

Fuente: arXiv
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Main Authors: Lejay, Antoine, Mazzonetto, Sara
Format: Preprint
Published: 2022
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author Lejay, Antoine
Mazzonetto, Sara
author_facet Lejay, Antoine
Mazzonetto, Sara
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2207_13954
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Beyond the delta method
Lejay, Antoine
Mazzonetto, Sara
Statistics Theory
Probability
Primary 62F12, Secondary 62F03, 62M02, 26B10
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.
title Beyond the delta method
topic Statistics Theory
Probability
Primary 62F12, Secondary 62F03, 62M02, 26B10
url https://arxiv.org/abs/2207.13954