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State space models on special manifolds. (English) Zbl 1099.62098

Summary: This paper concerns modeling time series observations in state space form considered on 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62F15 Bayesian inference
62H11 Directional data; spatial statistics
60G20 Generalized stochastic processes
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