Recursive estimation in hidden Markov models
Recursive estimation in hidden Markov models
复制标题
隐马尔可夫模型中的递归估计
DOI：
10.1109/cdc.1997.652384
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Mevel
中科院分区：
文献类型：
--
作者：
Fraqois;LeGland;Laurent;Mevel
我们考虑一个隐马尔可夫模型（HMM）与多维观测，其中的系数（转移概率矩阵，观测条件密度）取决于一些未知的参数。我们研究了两种递归估计量（递归最大似然估计量（RMLE）和递归条件最小二乘估计量（RCLSE））在观测值数量增加到无穷大时的渐进行为。首先，我们给出了这两种非递归估计的对比函数，并证明了这两种非递归估计的a.s.收敛性。对应的对比度函数的固定点的集合。其次，我们证明了这两个递推估计是渐近正态的。
We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal.