Convergence rate of maximum likelihood estimator of parameter in stochastic partial differential equation

• Published in: Journal of the Korean Statistical Society Vol. 44; no. 2; pp. 312 - 320
• Main Authors: Kim, Yoon Tae, Park, Hyun Suk
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.06.2015; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Cylindrical Brownian motion; Malliavin calculus; Maximum likelihood estimator; Multiple stochastic integral; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Stochastic partial differential equation; 통계학; Maximum likelihood estimator; Cylindrical Brownian motion; 60H30; Multiple stochastic integral; 60H07; Stochastic partial differential equation; Malliavin calculus
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2015.01.001

Using the recent results obtained by combining Malliavin calculus and Stein’s method, we study the rate of convergence of the distribution of the maximum likelihood estimator of a parameter appearing in a stochastic partial differential equation. The aim of this paper is to develop the new techniques, allowing us to improve the rate, given by Mishra and Prakasa Rao (2004), to O(1/N).