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Nonlocal Optimum Design

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Design of Experiments in Nonlinear Models

Part of the book series: Lecture Notes in Statistics ((LNS,volume 212))

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Abstract

The design criteria considered in Chap. 5 for nonlinear models are local, in the sense that they depend on the choice of a prior nominal value θ 0 for the model parameters θ.

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Notes

  1. 1.

    In a finite setting, ∑ i = 1 M μ i ϕ(ξ; θ (i)) can be interpreted as the Lagrange function for the maximization of ϕ MmO ( ⋅) with μ = (μ 1, …, μ M ) the vector of Lagrange multipliers, restricted to sum to one; see Li and Fang [1997].

  2. 2.

    The term adaptive design would thus be more appropriate to describe the kind of problem we shall deal with, which has strong connections with adaptive control; see, e.g., Pronzato [2008]. Sequential design remains the usual denomination in the literature, however.

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Authors and Affiliations

  1. French National Center for Scientific Research (CNRS), University of Nice, Sophia Antipolis, France

    Luc Pronzato

  2. Department of Applied Mathematics and Statistics, Comenius University, Bratislava, Slovakia

    Andrej Pázman

Authors
  1. Luc Pronzato
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  2. Andrej Pázman
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Pronzato, L., Pázman, A. (2013). Nonlocal Optimum Design. 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_8

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