New Kolmogorov bounds in the CLT for random ratios and applications.

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. • We provide a new Kolmogorov bound in the CLT for a ratio of Gaussian functionals. • This upper bound is expressed in terms of the third and fourth cumulants. • We apply our approach to the drift estimation of an Ornstein–Uhlenbeck process. [ABSTRACT FROM AUTHOR]