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Linear statistical models and stochastic realization theory

  • Lorenzo Finesso
  • Giorgio Picci
Session 8 Identification And Detection
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)

Abstract

The problem of representing a given gaussian zero mean random vector y by linear statistical models is considered. This is a concrete formulation of a simple stochastic realization problem. Let y=[y′1],y′2]′ be any partition of y into two disjoint subvectors y1, y2. It is shown that to every random vector x, making y1 and y2 conditionally independent given x there corresponds an (essentially unique) model of y of the form
$$\begin{gathered}y_1 = H_1 x + n_1 \hfill \\y_2 = H_2 x + n_2 \hfill \\\end{gathered} $$
(0)
where H1 and H2 are deterministic matrices, n1 and n2 are mutually independent noise terms and each ni(i=1,2) is independent of x. The family of all realizations of y of the form (0) is analyzed both probabilistically and from the point of view of explicit computation of the parameters. Possible applications especially to the theory of Factor Analysis are discussed.

Keywords

Random Vector Canonical Form Stochastic System Internal Model Minimal Realization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Lorenzo Finesso
    • 1
  • Giorgio Picci
    • 2
  1. 1.Ladseb-C.N.R.PadovaItaly
  2. 2.Istituto di Elettrotecnica ed ElettronicaPadovaItaly

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