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Sequential nonlinear estimation with nonaugmented priors

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Abstract

How can the basic compatibility of theory and observations be investigated for nonlinear processes without requiring stochastic characterizations for residual error terms? The present paper proposes a flexible least-cost approach. For each possible estimatex for the sequence of process states, letc D (x) andx M(x) denote the costs incurred for deviations away from the prior dynamic specifications and prior measurement specifications, respectively. Define the cost-efficiency frontier to be the greatest lower bound for the set of all possible cost pairs [c D (x),c M(x)], conditional on the given observations. State sequence estimatesx that attain the cost-efficiency frontier indicate the possible ways that the actual process could have developed over time in a manner minimally incompatible with the prior dynamic and measurement specifications. An algorithm is developed for the exact sequential updating of the cost-efficient state sequence estimates as the duration of the process increases and additional observations are obtained.

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Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, University of Southern California, Los Angeles, California

    R. Kalaba (Professor)

  2. Modelling Research Group, Department of Economics, University of Southern California, Los Angeles, California

    L. Tesfatsion (Associate Professor)

Authors
  1. R. Kalaba
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  2. L. Tesfatsion
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Additional information

A preliminary version of this paper (Ref. 1) was presented at the June 1986 Summer Econometric Society Meeting at Duke University. The authors are grateful to I. Adelman, E. Massoumi, S. Mittnik, H. C. Quirmbach, A. Zellner, and especially to R. Huss for helpful comments.

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Kalaba, R., Tesfatsion, L. Sequential nonlinear estimation with nonaugmented priors. J Optim Theory Appl 60, 421–438 (1989). https://doi.org/10.1007/BF00940346

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