论文标题
最佳浆果esséen以$α$ -BROWNIAN BRICGE中的漂移参数的最大似然估计
Optimal Berry-Esséen bound for Maximum likelihood estimation of the drift parameter in $ α$-Brownian bridge
论文作者
论文摘要
令$ t> 0，α> \ frac12 $。在本文中，我们考虑定义为$ dx_t =-α\ frac {x_t} {t-t} dt+dt+dw_t，〜0 \ 0 \ leq t <t $，其中$ w $是标准的布朗尼运动。我们根据连续观察$ \ {x_s，0 \ leq s \ leq t \} $作为$ t \ uparrow t $，研究参数$α$ $α$的最大似然估计器（MLE）的最佳收敛速率。我们证明，MLE中中央限制定理的kolmogorov距离的最佳速率由$ \ frac {1} {\ sqrt {\ sqrt {| \ log（t-t-t）|}} $，为$ t \ uparrow t $。首先，我们分别使用\ cite {kp-jva}的推论1和推论的2分，然后使用相同速度的下限进行计算。
Let $T>0,α>\frac12$. In the present paper we consider the $α$-Brownian bridge defined as $dX_t=-α\frac{X_t}{T-t}dt+dW_t,~ 0\leq t< T$, 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 $ α$ based on the continuous observation $\{X_s,0\leq s\leq t\}$ as $t\uparrow T$. We prove that an optimal rate of Kolmogorov distance for central limit theorem on the MLE is given by $\frac{1}{\sqrt{|\log(T-t)|}}$, 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 \cite{kp-JVA}, respectively.
