Local asymptotic mixed normality for discretely observed non-recurrent Ornstein–Uhlenbeck processes
Local asymptotic mixed normality for discretely observed non-recurrent Ornstein–Uhlenbeck processes
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DOI：
10.1007/s10463-010-0307-4
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发表时间：
2012-02
影响因子：
1
通讯作者：
Y. Shimizu
中科院分区：
文献类型：
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作者：
Y. Shimizu
考虑具有未知漂移和扩散参数的非常Ornstein-Uhlenbeck过程。我们的目的是从具有一定渐近性的离散观测值中联合估计参数。我们证明了离散样本的似然比具有一致的LAMN性质，并且某种近似的极大似然估计在渐近最大集中概率意义下是渐近最优的。在遍历的情况下，估计量也是渐近有效的。
Consider non-recurrent Ornstein–Uhlenbeck processes with unknown drift and diffusion parameters. Our purpose is to estimate the parameters jointly from discrete observations with a certain asymptotics. We show that the likelihood ratio of the discrete samples has the uniform LAMN property, and that some kind of approximated MLE is asymptotically optimal in a sense of asymptotic maximum concentration probability. The estimator is also asymptotically efficient in ergodic cases.