The Statistical Theory of Linear Systems. Cet article n’est pas disponible.The Statistical Theory of Linear Systems

This volume discusses closely the making of good models from observations, offering an interdisciplinary treatment of the subject. Focusing on linear dynamic systems evolving in discrete time, it examines their importance in the development of new applications in various fields, pointing out their interconnections and potential use for workers in several disciplines. Discussions cover the significant progress made in understanding the algebraic and topological structure of linear dynamic systems, work originating in the fields of systems and control engineering, the application of the scalar output case in modelling, the development of algorithms for on-line and real-time calculations, and recent work by statistical time-series analysts on theory and algorithms for off-line calculation. The required asymptotic theory associated with estimation procedures is also examined.

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.