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Article information
2019 , Volume 24, ¹ 5, p.90-108
Shary S.P.
On a variability measure for estimates of parameters in the statistics of interval data
The article presents a possible construction for quantitative variability measure of parameter estimates in the data fitting problem under interval uncertainty. It is designed to show the degree of variability and ambiguity of the estimate. The problem is important since the answer to the data fitting problem may be not unique under the uncertainty of interval data. Otherwise, the problem may have a whole set of such feasible answers, and an estimate of the size of this set can serve as a variability measure of the solution. So-called maximum compatibility method is considered as a method for evaluating the parameters of the function. An estimate of the parameters is taken as the maximum point of a special “recognizing functional”, i.e. a certain function that characterizes compatibility of the estimate with interval empirical data. Then the variability measure is simply computed as the product of several values found in the solution of the data fitting problem. These values are maximum of the recognizing functional, minimum of the condition number of the data matrix and the ratio of the norm of the parameter estimate to the norm of the vector of function values. A derivation of the new variability measure is given, and its application is illustrated with specific examples. In conclusion, the article discusses the motivation and interpretation of the new variability measure from the point of view of other known data characteristics.
[full text]
Keywords: data fitting problem, interval data uncertainty, strong compatibility of parameters and data, variability measure
doi: 10.25743/ICT.2019.24.5.008
Author(s):
Shary Sergey Petrovich
Dr. , Senior Scientist
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
Phone Office: (3832) 30 86 56
E-mail: shary@ict.nsc.ru
SPIN-code: 9938-9344 References:
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Bibliography link:
Shary S.P. On a variability measure for estimates of parameters in the statistics of interval data // Computational technologies. 2019. V. 24. ¹ 5. P. 90-108
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