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

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; 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