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Beyond the delta method


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.
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hal-03738371 , version 1 (26-07-2022)



Antoine Lejay, Sara Mazzonetto. Beyond the delta method. 2022. ⟨hal-03738371⟩
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