Abstract
This paper is devoted to the problem of fitting input-output data by a modeling function, linear in its parameters, in the presence of interval-bounded errors in output variable. A method for outlier detection is proposed. Another issue under consideration is the comparative simulation study of the well-known statistical point estimates (least squares, maximum likelihood) and point estimates calculated as the center of interval hull of uncertainty set. The results of the study allow us to draw the conclusion that non-statistical interval based estimation is a competitive alternative to statistical estimation in some cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belov, V. M., Sukhanov, V. A., Guzeev, V. V., and Unger, F. G.: Estimation of Linear Physicochemical Dependencies by Rectangle of Uncertainty Center Method, Izvestia Vuzov. Fizika 8 (1991), pp. 35–45 (in Russian).
Borodyuk, V. P.: Comment I to the Article by Voshchinin A. P., Bochkov A. F., Sotirov G. R. “A Method for Data Analysis in the Presence of Interval Non-Statistical Error,” Zavodskaya Laboratoriya 7 (56) (1990), pp. 81–83 (in Russian).
Eremin, I. I.: Contradictory Models of Optimal Planning, Nauka, Moscow, 1988 (in Russian).
Kantorovich, L. V.: On Some New Approaches to Numerical Methods and Observation Processing, Sib. Math. Zhurnal 5 (3) (1962), pp. 701–709 (in Russian).
Milanese, M. and Belforte, G.: Estimation Theory and Uncertainty Intervals Evaluation in Presence of Unknown but Bounded Errors: Linear Families of Models and Estimators, IEEE Transactions on Automatic Control 2 (27) (1982), pp. 408–414.
Novitskii, P. V. and Zograph, I. A.: Estimating the Measurement Errors, Energoatomizdat, Leningrad, 1985 (in Russian).
Orlov, A. I.: How Often Is the Observation Normal? Zavodskaya Laboratoriya 7 (57) (1991), pp. 64–66 (in Russian).
Oskorbin, N. M., Maksimov, A. V., and Zhilin, S. I.: Construction and Analysis of Empirical Dependencies by Uncertainty Center Method, Transactions of Altai State University 1 (1998), pp. 35–38 (in Russian).
Spivak, S. I.: Detailed Analysis of Application of Linear Programming Methods to Estimation of Parameters of Kinetic Models, in: Matematicheskie Problemy Khimii 2 (1975), VC SO AN SSSR, Novosibirsk, pp. 35–42 (in Russian).
Rodionova, O. Ye. and Pomerantsev, A. L.: Antioxidants Activity Prediction Using DSC Measurements and SIC Data Processing, in: Proceedings of Second Conference on Experimental Methods in Physics of Heterogeneous Condensed Media, Barnaul, 2001, pp. 239–246.
Voshchinin, A. P., Bochkov, A. F., and Sotirov G. R.: A Method for Data Analysis in the Presence of Interval Non-Statistical Error, Zavodskaya Laboratoriya 7 (56) (1990), pp. 76–81 (in Russian).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhilin, S.I. On Fitting Empirical Data under Interval Error. Reliable Comput 11, 433–442 (2005). https://doi.org/10.1007/s11155-005-0050-3
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11155-005-0050-3