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Optimal Berry–Esseen bound for statistical estimations and its application to SPDE

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  • Kim, Yoon Tae
  • Park, Hyun Suk

Abstract

We consider asymptotically normal statistics of the form Fn/Gn, where Fn and Gn are functionals of Gaussian fields. For these statistics, we establish an optimal Berry–Esseen bound for the Central Limit Theorem (CLT) of the sequence Fn/Gn is φ(n) in the following sense: there exist constants 0

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  • Kim, Yoon Tae & Park, Hyun Suk, 2017. "Optimal Berry–Esseen bound for statistical estimations and its application to SPDE," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 284-304.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:284-304
    DOI: 10.1016/j.jmva.2017.01.006
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    References listed on IDEAS

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    1. J. Pfanzagl, 1971. "The Berry-Esseen bound for minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 17(1), pages 82-91, December.
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    1. Yoon-Tae Kim & Hyun-Suk Park, 2021. "An Edgeworth Expansion for the Ratio of Two Functionals of Gaussian Fields and Optimal Berry–Esseen Bounds," Mathematics, MDPI, vol. 9(18), pages 1-23, September.

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