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Estimation of parameter bounds from bounded-error data: a survey

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  • Walter, Eric
  • Piet-Lahanier, Hélène

Abstract

Set-membership techniques for estimating parameters from uncertain data are reviewed. Contrary to the prevailing usage, the error in the data is not considered as a random variable with known or parameterized probability density function. Instead, the error is assumed to lie between some known upper and lower bounds. One is then looking for a suitable characterization of the set of all parameter vectors consistent with the model structure, data, and bounds on the errors.

Suggested Citation

  • Walter, Eric & Piet-Lahanier, Hélène, 1990. "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 449-468.
    • Handle: RePEc:eee:matcom:v:32:y:1990:i:5:p:449-468
    DOI: 10.1016/0378-4754(90)90002-Z
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    References listed on IDEAS

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    1. Clement, Thierry & Gentil, Sylviane, 1988. "Reformulation of parameter identification with unknown-but-bounded errors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(3), pages 257-270.
    2. Pronzato, Luc & Walter, Eric, 1990. "Experiment design for bounded-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 571-584.
    3. Tempo, R. & Vicino, A., 1990. "Optimal algorithms for system identification: a review of some recent results," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 585-595.
    4. Clement, Thierry & Gentil, Sylviane, 1990. "Recursive membership set estimation for output-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 505-513.
    5. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.
    6. Broman, V. & Shensa, M.J., 1990. "A compact algorithm for the intersection and approximation of N-dimensional polytopes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 469-480.
    7. Norton, J.P. & Mo, S.H., 1990. "Parameter bounding for time-varying systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 527-534.
    8. Rao, Ashok K. & Huang, Yih-Fang, 1990. "Recent developments in optimal bounding ellipsoidal parameter estimation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 515-526.
    9. Piet-Lahanier, H. & Walter, E., 1990. "Characterization of non-connected parameter uncertainty regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 553-560.
    10. Walter, E. & Piet-Lahanier, H. & Happel, J., 1986. "Estimation of non-uniquely identifiable parameters via exhaustive modeling and membership set theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 28(6), pages 479-490.
    11. Pronzato, Luc & Walter, Eric & Venot, Alain & Lebruchec, Jean-Francois, 1984. "A general-purpose global optimizer: Implimentation and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(5), pages 412-422.
    12. Keesman, Karel, 1990. "Membership-set estimation using random scanning and principal component analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 535-543.
    13. Belforte, G. & Bona, B. & Cerone, V., 1990. "Identification, structure selection and validation of uncertain models with set-membership error description," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 561-569.
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    Citations

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    Cited by:

    1. Jaulin, Luc & Walter, Eric, 1993. "Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 123-137.
    2. Marco Stenborg Petterson & David Seim & Jesse M. Shapiro, 2023. "Bounds on a Slope from Size Restrictions on Economic Shocks," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 552-572, August.
    3. Piet-Lahanier, H. & Walter, E., 1990. "Exact recursive characterization of feasible parameter sets in the linear case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 495-504.
    4. Enríquez, R. & Jiménez, M.J. & Heras, M.R., 2017. "Towards non-intrusive thermal load Monitoring of buildings: BES calibration," Applied Energy, Elsevier, vol. 191(C), pages 44-54.
    5. Shary, Sergey P., 1995. "Solving the linear interval tolerance problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 53-85.
    6. da Silva, Ivan N. & de Arruda, Lucia V.R. & do Amaral, Wagner C., 1999. "A novel approach to robust parameter estimation using neurofuzzy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(3), pages 251-268.
    7. Piet-Lahanier, H. & Walter, E., 1990. "Characterization of non-connected parameter uncertainty regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 553-560.
    8. Piet-Lahanier, Hélène & Veres, Sándor M. & Walter, Eric, 1992. "Comparison of methods for solving sets of linear inequalities in the bounded-error context," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(6), pages 515-524.
    9. Mo, S.H. & Norton, J.P., 1990. "Fast and robust algorithm to compute exact polytope parameter bounds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 481-493.

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    2. Pronzato, Luc & Walter, Eric, 1990. "Experiment design for bounded-error models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 32(5), pages 571-584.
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