We develop techniques for determining an explicit Berry–Esseen bound in the Kolmogorov distance for the normal approximation of a ratio of Gaussian functionals. We provide an upper bound in terms of the third and fourth cumulants, using some novel techniques and sharp estimates for cumulants. As applications, we study the rate of convergence of the distribution of discretized versions of minimum contrast and maximum likelihood estimators of the drift parameter of the Ornstein–Uhlenbeck process. Moreover, we derive upper bounds that are strictly sharper than those available in the literature.

中文翻译：

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CLT 中随机比率和应用的新柯尔莫哥洛夫界限

我们开发了确定柯尔莫哥洛夫距离中显式 Berry-Esseen 界的技术，以实现高斯泛函比率的正态逼近。我们使用一些新颖的技术和对累积量的精确估计，提供了第三和第四累积量的上限。作为应用，我们研究 Ornstein-Uhlenbeck 过程的漂移参数的最小对比度和最大似然估计的离散版本分布的收敛速度。此外，我们得出的上限比文献中提供的上限更严格。