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The Statistical Theory of Linear Systems

The Statistical Theory of Linear Systems


Part of Classics in Applied Mathematics

  • Date Published: April 2012
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9781611972184

£ 75.00

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About the Authors
  • 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.

    • Updated edition of a classic text that describes advances in the field since its original publication
    • Covers the fundamental topics to an extent not often found in texts on the same subject
    • Contains an instructive interweaving of structure theory and statistical theory of linear systems
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    Product details

    • Date Published: April 2012
    • format: Paperback
    • isbn: 9781611972184
    • length: 400 pages
    • dimensions: 228 x 151 x 21 mm
    • weight: 0.58kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    Preface to the Classics edition
    Introduction to the Classics edition
    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
    Author index
    Subject index.

  • Authors

    E. J. Hannan
    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, Technische Universität Wien, Austria
    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.

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