Maximum likelihood estimator for skew Brownian motion: The convergence rate
研究了偏斜布朗运动偏斜参数的最大似然估计的渐近性质，证明了其渐近服从混合正态分布，收敛速度与局部时有关，并给出了估计量的级数展开。
Abstract We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence of estimators for the SBM, we prove a conjecture left open that the MLE has asymptotically a mixed normal distribution involving the local time with a rate of convergence of order . We also give a series expansion of the MLE and study the asymptotic behavior of the score and its derivatives, as well as their variation with the skewness parameter. In particular, we exhibit a specific behavior when the SBM is actually a Brownian motion, and quantify the explosion of the coefficients of the expansion when the skewness parameter is close to or 1.