Asymptotic criteria for designs in nonlinear regression with model errors

Abstract : We derive bounds for the design optimality criteria under the assumption that the supposed regression model $y (x_k) = \eta(x_k, \theta)+\varepsilon_k, k = 1, 2, ...$ does not correspond to the true one. The investigation is based on the asymptotic properties of the LSE of $\theta$, and full proofs of these properties are presented under the assumption that the sequence of design points $\{x_k\}_{k=1}^\infty$ is randomly sampled according to a design measure $\xi$. The bounds and the asymptotic properties are related to the intrinsic measure of nonlinearity of the model.
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Andrej Pazman, Luc Pronzato. Asymptotic criteria for designs in nonlinear regression with model errors. Mathematica Slovaca, 2006, 56 (5), pp.543-553. ⟨hal-00158853⟩

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