Let \(T>0,\alpha >\frac{1}{2}\). In the present paper we consider the \(\alpha \)-Brownian bridge defined as \(dX_t=-\alpha \frac{X_t}{T-t}dt+dW_t,\, 0\le t< T\), where W is a standard Brownian motion. We investigate the optimal rate of convergence to normality of the maximum likelihood estimator (MLE) for the parameter \( \alpha \) based on the continuous observation \(\{X_s,0\le s\le t\}\) as \(t\uparrow T\). We prove that an optimal rate of Kolmogorov distance for central limit theorem on the MLE is given by \(\frac{1}{\sqrt{\vert \log (T-t)\vert }}\), as \(t\uparrow T\). First we compute an upper bound and then find a lower bound with the same speed using Corollary 1 and Corollary 2 of Kim et al. (J Multivar Anal 155:284–304, 2017b) respectively.

让\（T> 0，\ alpha> \ frac {1} {2} \）。在本文中，我们考虑\（\ alpha \）-布朗桥定义为\（dX_t =-\ alpha \ frac {X_t} {Tt} dt + dW_t，\，0 \ le t <T \），其中W是标准的布朗运动。我们基于连续观察\（\ {X_s，0 \ le s \ le t \} \）作为\来调查参数\（\ alpha \）的最大似然估计量（MLE）的正态性的最优收敛速率。（t \ uparrow T \）。我们证明，对于MLE上的中心极限定理，Kolmogorov距离的最佳速率由\（\ frac {1} {\ sqrt {\ vert \ log（Tt）\ vert}} \\）给出，如\（t \ uparrow T \）。首先，我们使用Kim等人的推论1和推论2计算出一个上限，然后以相同的速度找到一个下限。（J Multivar Anal 155：284–304，2017b）。