Successive Approximation of Nonlinear Confidence Regions (SANCR)

Abstract : In parameter estimation problems an important issue is the approximation of the confidence region of the estimated parameters. Especially for models based on differential equations, the needed computational costs require particular attention. For this reason, in many cases only linearized confidence regions are used. However, despite the low computational cost of the linearized confidence regions, their accuracy is often limited. To combine high accuracy and low computational costs, we have developed a method that uses only successive linearizations in the vicinity of an estimator. To accelerate the process, a principal axis decomposition of the covariance matrix of the parameters is employed. A numerical example illustrates the method.
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Lorena Bociu; Jean-Antoine Désidéri; Abderrahmane Habbal. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. Springer International Publishing, IFIP Advances in Information and Communication Technology, AICT-494, pp.180-188, 2016, System Modeling and Optimization. 〈10.1007/978-3-319-55795-3_16〉
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Thomas Carraro, Vladislav Olkhovskiy. Successive Approximation of Nonlinear Confidence Regions (SANCR). Lorena Bociu; Jean-Antoine Désidéri; Abderrahmane Habbal. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. Springer International Publishing, IFIP Advances in Information and Communication Technology, AICT-494, pp.180-188, 2016, System Modeling and Optimization. 〈10.1007/978-3-319-55795-3_16〉. 〈hal-01626907〉

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