Abstract
This paper establishes necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators. It further gives several easy to verify sufficient conditions. These conditions are then used to show that the assumptions hold for large classes of distributions with regularly varying tails. This includes classes for which asymptotic normality had not been previously verified.
Acknowledgements
The authors wish to thank Dr. Zhiyi Zhang for suggesting the problem and the editor and two anonymous referees, whose comments lead to an improvement in the presentation of this paper.
Citation
Jie Chang. Michael Grabchak. "Necessary and sufficient conditions for the asymptotic normality of higher order Turing estimators." Bernoulli 29 (4) 3369 - 3395, November 2023. https://doi.org/10.3150/23-BEJ1587
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