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

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)O(1/N).