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Identifiability, Estimability, and Extended Optimality Criteria

  • Luc Pronzato
  • Andrej Pázman
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Part of the Lecture Notes in Statistics book series (LNS, volume 212)

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.

Keywords

Design Measure Exact Design Intrinsic Curvature Estimability Function Estimability Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Luc Pronzato
    • 1
  • Andrej Pázman
    • 2
  1. 1.French National Center for Scientific Research (CNRS)University of NiceSophia AntipolisFrance
  2. 2.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia

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