Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

• Published in: Journal of the Korean Statistical Society Vol. 47; no. 3; pp. 364 - 378
• Main Authors: Kim, Yoon Tae, Park, Hyun Suk
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.09.2018; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Berry–Esseen bound; Central limit theorem; Kolmogorov distance; Malliavin calculus; Maximum likelihood estimator; Multiple stochastic integral; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Stein’s method; Stochastic partial differential equations; 통계학; 60F25; Maximum likelihood estimator; Kolmogorov distance; Stochastic partial differential equations; Stein’s method; Central limit theorem; Berry–Esseen bound; Multiple stochastic integral; 60H07; Malliavin calculus; Berry-Esseen bound
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2018.04.003

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter θ appearing in parabolic SPDEs of the form duϵ(t,x)=(A0+θA1)uϵ(t,x)dt+ϵdW(t,x),where A0 andA1 are partial differential operators, W is a cylindrical Brownian motion (CBM) and ϵ↓0. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.