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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...

Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, JoĂŁo Hespanha covers the key topics of the field i...

This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant...

Recent years have seen a significant rise of interest in max-linear theory and techniques. In addition to providing the linear-algebraic background in the field of tropical mathematics, max-algebra provides mathematical theory and techniques for solving v...

Concise exposition of realizability theory as applied to continous linear systems, specifically to the operators generated by physical systems as mappings of stimuli into responses. Many problems included. ...

This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant...

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-s...

"Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties ...

This introduction to the important interplay between nonlinear dynamics and statistical theories for geophysical flows is designed for a multi-disciplinary audience ranging from graduate students to senior researchers. Novel applications of information th...

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...