State space models on special manifolds
- 作者：Yasuko Chikuse
- 关键词：State space model ; Stiefel manifold ; Grassmann manifold ; Matrix Langevin distributions ; Posterior mode estimation ; Iterative method
- 刊名：Journal of Multivariate Analysis
- 出版年：2006
- 期刊代码：77_0047259x
- 类别：mt
- 出版时间：July 2006
- 卷：97
- 期：6
- 页码：1284-1294
- 文件大小：173 K
摘要
This paper concerns modeling time series observations in state space forms considered on the Stiefel and Grassmann manifolds. We develop a state space model relating the time series observations to a sequence of unobserved state or parameter matrices assuming the matrix Langevin noise processes on the Stiefel manifolds. We show a Bayes method for estimating the state matrices by the posterior modes. We consider a further extended state space model where two sequences of unobserved state matrices are involved. A simple state space model on the Grassmann manifolds with matrix Langevin noise processes is also investigated.