An improved Kolmogorov bound for approximate maximum likelihood estimators for the α-Brownian bridge

We derive a new explicit upper bound of the Kolmogorov distance for the rates of convergence of the distribution of two approximative maximum likelihood estimators of the drift coefficient in a discretely-observed α-Brownian bridge. Specifically, we provide an upper bound that is strictly sharper than the one available in the literature in (Es-Sebaiy et al. in J. Stoch. Anal. 2(2):8, 2021). Moreover, we obtain a bound that is potentially of the same order as the optimal bound obtained by (Es-Sebaiy and Moustaaid in J. Korean Stat. Soc. 50:403–418, 2021) in the case of continuous observations.