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Optimal Conditional Estimation: Average Case Setting

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  • B. Kacewicz

    (University of Mining and Metallurgy)

Abstract

We consider an estimation problem which appears in the identification of systems by means of restricted complexity models: find the optimal approximation to an element of a linear normed space (a system) based on noisy information, subject to the restriction that approximations (models) can be selected from a prescribed subspace M of the problem element space. In contrast to the worst-case optimization criterion, which may be pessimistic, in this paper the quality of an identification algorithm is measured by its local average performance. Two types of local average errors are considered: for a given information (measurement) y and for a given unknown element x, the latter in two versions. For a wide spectrum of norms in the measurement space, we define an optimal algorithm and give expressions for its average errors which show the dependence on information, information errors, unmodelled dynamics, and norm in the measurement space.

Suggested Citation

  • B. Kacewicz, 2001. "Optimal Conditional Estimation: Average Case Setting," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 649-666, June.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:3:d:10.1023_a:1017524023577
    DOI: 10.1023/A:1017524023577
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    References listed on IDEAS

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    1. A. Garulli & B. Z. Kacewicz & A. Vicino & G. Zappa, 1999. "Reliability of Projection Algorithms in Conditional Estimation," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 1-14, April.
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