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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. ## About book:

## About file:

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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; and approximation by rational functions.

This edition includes an extensive new introduction that outlines central ideas and features of the subject matter, as well as 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.

**Audience:** Researchers and graduate students studying time series statistics, systems identification, econometrics, and signal processing will find this book useful for its comprehensive theoretical analysis and, in particular, for its interweaving of foundational information on structure theory and statistical analysis of linear systems.

**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

- Series:
**Classics in Applied Mathematics 70** - Author:
**E. J. Hannan, Manfred Deistler** - Year:
**2012** - Publisher:
**SIAM** - Language:
**English** - ISBN:
**1611972183,978-1-611972-18-4**

- File size:
**15 597 656** - Format:
**pdf**

Security code:

This text is an extensive revision of the author's highly successful text, Linear Systems Theory and Design. In the third edition, the author is revising his formerly more theoretical approach to the topic of linear systems, choosing instead a more genera...

Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to p...

This volume is the second of the three volume publication containing the proceedings of the 1989 International Symposium on the MathematÂ ical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989 The Int...

This book concentrates on the problem of accurate modeling of linear systems. It presents a thorough description of a method of modeling a linear dynamic invariant system by its transfer function. The first two chapters provide a general introduction and ...

Iterative Methods for Linear Systems offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet c...

Statistical Theory of Signal Detection contents signals and filters, noise, hypothesis testing, detection of a known signal, detection of signals of unknown phase, digital communications, detection by multiple observations, the estimation of signal parame...

More and more, the advanced technological systems of today rely on sophisticated control systems designed to assure greater levels of safe operation while optimizing performance. Rather than assuming always perfect conditions, these systems require adapti...

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with ...

This book treats the random mechanical and acoustical vibrations of deterministic and statistical dynamic systems, in the low and high frequency range. The following topics are discussed in great detail:Vibrations of deterministic linear mechanical dynami...

This volume contains the papers presented at the 11th SDL Forum, Stuttgart. As well as the papers, the 11th SDL Forum also hosted a system design competition sponsored by Solinet with a cash prize for the â€śbestâ€ť design. This follows a similar competition ...

The four-volume set LNCS 3480-3483 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2005, held in Singapore in May 2005.The four volumes present a total of 540 papers selected from a...

This book is about infant mortality decline, the rise of the infant welfare movement, outcomes in terms of changing priorities in child health and what happened to mothers and babies. Infant welfare raised public awareness but did not contribute as powerf...

Develops new and intriguing insights into globalization theory and internationalization practice, expanding the investigation of East Asian values and contexts in comparison and separate from Western-dominant thoughts of globalization and internationaliza...