Abstract
Among the major difficulties that one may encounter when estimating parameters in a nonlinear model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations, and the presence of local optimizers of the estimation criterion. Classically, those issues are ignored at the design stage: the designs of Chap. 5 are based on asymptotic local properties of the estimator; the approaches of Chap. 6 make use of an assumption (\({\rm H}_{\mathcal{S}}\), p. 183) which allows us to avoid these difficulties. The main message of this chapter is that estimability issues can be taken into account at the design stage, through the definition of suitable design criteria. This forms a difficult area, still under development. Several new notions will be introduced, and a series of examples will illustrate the importance of the geometry of the model.
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Notes
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This is true for almost any θ (in the sense of zero Lebesgue measure on compact subsets on ℝ 3); notice that the model is not identifiable for θ 1 = 0.
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Pronzato, L., Pázman, A. (2013). Identifiability, Estimability, and Extended Optimality Criteria. In: Design of Experiments in Nonlinear Models. Lecture Notes in Statistics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6363-4_7
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