The Statistical Theory of Linear Systems

Originally published in 1988, The Statistical Theory of Linear Systems deals with identification (in the sense of obtaining a model from data) of multi-input and multi-output linear systems, in particular systems in ARMAX and state space form. The book emphasizes the underlying theory. It covers: Structure theory, in particular realization and parameterization of linear systems, with special emphasis on the analysis of properties of parameter spaces and parameterizations relevant for estimation and model selection. Gaussian maximum likelihood estimation of the real-valued parameters of linear systems, with an emphasis on asymptotic theory Model selection, in particular order estimation, by information criteria such as AIC or BIC, with an emphasis on asymptotic theory. Procedures for calculation of estimates. Approximation by rational functions.