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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:155

Article

Kim, Yoon Tae¹  Park, Hyun Suk¹ 

[1] Hallym Univ, Dept Stat, Chunchon 200702, Gangwon, South Korea

关键词: Berry-Esseen bound;    Central limit theorem;    Kolmogorov distance;    Malliavin calculus;    Maximum likelihood estimator;    Multiple stochastic integral;    Stein's method;    Stochastic partial differential equations;   

DOI  :  10.1016/j.jmva.2017.01.006

来源: Elsevier

【 摘 要 】

We consider asymptotically normal statistics of the form F-n/G(n), where F-n and G(n) are functionals of Gaussian fields. For these statistics, we establish an optimal Berry-Esseen bound for the Central Limit Theorem (CLT) of the sequence F-n/G(n), is phi (n) in the following sense: there exist constants 0 < c < C < infinity such that c <= d(Kol) (F-n/G(n), Z)/phi(n) <= C, where d(Kol) (F-n, Z) = sup(z is an element of R). vertical bar Pr(F-n, <= z) - Pr(Z <= z)vertical bar. As an example, we find an optimal Berry-Esseen bound for the CLT of the maximum likelihood estimators for parameters occurring in parabolic stochastic partial differential equations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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