The Statistical Theory of Linear Systems
Published on 31. May 2012
Book
Paperback/Softback
400 pages
978-1-61197-218-4 (ISBN)
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Description
Originally published in 1988, this classic text treats the identification of noisy (multi-input and multi-output) linear systems, particularly systems in ARMAX and state space form. The book covers structure theory, including identifiability, realisation and parameterisation of linear systems; analysis of topological and geometrical properties of parameter spaces and parameterisations for estimation and model selection; Gaussian maximum likelihood estimation of real-valued parameters of linear systems; model selection; calculation of estimates; and approximation by rational transfer functions. This edition includes an extensive new introduction that outlines developments since the book's original publication, such as subspace identification, data-driven local coordinates and the results on post-model-selection estimators. It also provides a section of errata and an updated bibliography. Researchers and graduate students studying time series statistics, systems identification, econometrics and signal processing will find this book useful for its interweaving of foundational information on structure theory and statistical analysis of linear systems.
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Persons
Author
E. J. Hannan (1921-1994) was Professor of Statistics at the Australian National University in Canberra. He was a pioneer of modern time series analysis and winner of both the Pitman Medal and the Thomas Ranken Lyle Medal. The Australian Academy of Sciences commemorates his work by awarding the Hannan Medal every two years to recognise achievements of Australians in pure mathematics, applied and computational mathematics and statistical science.
Manfred Deistler is Emeritus Professor at the Vienna University of Technology. He is a Fellow of the Econometric Society, the IEEE and the Journal of Econometrics. He is also a member of the Austrian Academy of Sciences.
Content
Preface to the Classics edition; Introduction to the Classics edition; Preface; Index of notations; 1. Linear systems and stationary processes; 2. Realization and parameterization of linear dynamic systems; 3. The Kalman filter; 4. Maximum likelihood estimation of ARMAX systems; 5. Estimating the order of a linear system; 6. Calculation of the estimates; 7. Approximation by rational transfer functions; References; Author index; Subject index.