Displaying similar documents to “Estimation in a model with infinite-dimensional nuisance parameter.”

Identification of parametric models with a priori knowledge of process properties

Krzysztof B. Janiszowski, Paweł Wnuk (2016)

International Journal of Applied Mathematics and Computer Science

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An approach to estimation of a parametric discrete-time model of a process in the case of some a priori knowledge of the investigated process properties is presented. The knowledge of plant properties is introduced in the form of linear bounds, which can be determined for the coefficient vector of the parametric model studied. The approach yields special biased estimation of model coefficients that preserves demanded properties. A formula for estimation of the model coefficients is derived...

On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy

Jurjen Duintjer Tebbens, Ctirad Matonoha, Andreas Matthios, Štěpán Papáček (2019)

Applications of Mathematics

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A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence...

A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation

D. Chapelle, A. Gariah, P. Moireau, J. Sainte-Marie (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...

Set-membership identifiability of nonlinear models and related parameter estimation properties

Carine Jauberthie, Louise Travé-Massuyès, Nathalie Verdière (2016)

International Journal of Applied Mathematics and Computer Science

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Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and...

Some Parameter Estimation Issues in Functional-Structural Plant Modelling

P.-H. Cournède, V. Letort, A. Mathieu, M. Z. Kang, S. Lemaire, S. Trevezas, F. Houllier, P. de Reffye (2011)

Mathematical Modelling of Natural Phenomena

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The development of functional-structural plant models has opened interesting perspectives for a better understanding of plant growth as well as for potential applications in breeding or decision aid in farm management. Parameterization of such models is however a difficult issue due to the complexity of the involved biological processes and the interactions between these processes. The estimation of parameters from experimental data by...

Variance function estimation via model selection

Teresa Ledwina, Jan Mielniczuk (2010)

Applicationes Mathematicae

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The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood...