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Linear statistical models and stochastic realization theory

  • Session 8 Identification And Detection
  • Conference paper
  • First Online:
Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((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.

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Author information

Authors and Affiliations

  1. Ladseb-C.N.R., Corso Stati Uniti 4, 35100, Padova, Italy

    Lorenzo Finesso

  2. Istituto di Elettrotecnica ed Elettronica, Via Gradenigo 6A, 35131, Padova, Italy

    Giorgio Picci

Authors
  1. Lorenzo Finesso
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  2. Giorgio Picci
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Editor information

A. Bensoussan J. L. Lions

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© 1984 Springer-Verlag

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Finesso, L., Picci, G. (1984). Linear statistical models and stochastic realization theory. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004973

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  • DOI: https://doi.org/10.1007/BFb0004973

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13551-7

  • Online ISBN: 978-3-540-39007-7

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