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The Statistical Theory of Linear Systems: (Classics in Applied Mathematics)

The Statistical Theory of Linear Systems: (Classics in Applied Mathematics)


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About the Book

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.


    Table of Contents:
    • Preface to the Classics Edition
    • Introduction to the Classics Edition
    • Preface
    • Index of Notations;Chapter 1: Linear Systems and Stationary Processes
    • Chapter 2: Realization and Parameterization of Linear Dynamic Systems
    • Chapter 3: The Kalman Filter
    • Chapter 4: Maximum Likelihood Estimation of Armax Systems
    • Chapter 5: Estimating the Order of a Linear System
    • Chapter 6: Calculation of the Estimates
    • Chapter 7: Approximation by Rational Transfer Functions
    • References
    • Author Index
    • Subject Index


      About the 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.


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      Product Details
      • ISBN-13: 9781611972184
      • Publisher: Society for Industrial & Applied Mathematics,U.S.
      • Publisher Imprint: Society for Industrial & Applied Mathematics,U.S.
      • Height: 229 mm
      • No of Pages: 425
      • Series Title: Classics in Applied Mathematics
      • Weight: 590 gr
      • ISBN-10: 1611972183
      • Publisher Date: 30 Apr 2012
      • Binding: Paperback
      • Language: English
      • Returnable: N
      • Spine Width: 21 mm
      • Width: 152 mm


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