The Berry-Esséen Upper Bounds of Vasicek Model Estimators

Abstract: The Berry-Ess\'{e}en upper bounds of moment estimators and least squares estimators of the mean and drift coefficients in Vasicek models driven by general Gaussian processes are studied. When studying the parameter estimation problem of Ornstein-Uhlenbeck (OU) process driven by fractional Brownian motion, the commonly used methods are mainly given by Kim and Park, they show the upper bound of Kolmogorov distance between the distribution of the ratio of two double Wiener-It^{o} stochastic integrals and the Normal distribution. The main innovation in this paper is extending the above ratio process, that is to say, the numerator and denominator respectively contain triple Wiener-It^{o} stochastic integrals at most. As far as we know, the upper bounds between the distribution of above estimators and the Normal distribution are novel.