论文标题
隐藏的马尔可夫模型，较高的噪声会导致较小的错误
Hidden Markov Model Where Higher Noise Makes Smaller Errors
论文作者
论文摘要
我们考虑了部分观察到的线性高斯系统的参数估计问题，该系统在状态和观察方程式中具有小声音。我们描述了MLE和BAYES估计量的渐近特性，其状态和观察噪声可能不平等。结果表明，两个估计器都是一致的，渐近地正常，均具有收敛力和渐近效率。该模型具有不寻常的特征：状态方程中较大的噪声会产生较小的估计误差。这些证明是基于对卡尔曼 - 布西过滤器和相关的riccati方程的渐近分析。
We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with state and observation noises of possibly unequal intensities. It is shown that both estimators are consistent, asymptotically normal with convergent moments and asymptotically efficient. This model has an unusual feature: larger noise in the state equation yields smaller estimation error. The proofs are based on asymptotic analysis of the Kalman-Bucy filter and the associated Riccati equation in particular.
