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**Minimax regression designs under uniform departure models.**
*(English)*
Zbl 0773.62053

Summary: Model robustness in optimal regression design is studied by introducing a family of nonparametric models, which are defined as neighborhoods of classical parametric models in terms of the uniform norm. Optimal designs are sought under a minimax criterion for estimating linear functionals on such models that may be put as integrals using measures of finite support.

A set of conditions equivalent to design optimality is derived using a Lagrangian principle applicable when the dimension is infinite and the function is not everywhere differentiable. From these conditions various optimal designs follow. Among them is the classical extrapolation design of J. Kiefer and J. Wolfowitz [Ann. Math. Statistics 30, 271- 294 (1959; Zbl 0090.114)] for Chebyshev regression, which is therefore model-robust against uniform departures. The conditions also shed light on other classical results of Kiefer and Wolfowitz and of others.

A set of conditions equivalent to design optimality is derived using a Lagrangian principle applicable when the dimension is infinite and the function is not everywhere differentiable. From these conditions various optimal designs follow. Among them is the classical extrapolation design of J. Kiefer and J. Wolfowitz [Ann. Math. Statistics 30, 271- 294 (1959; Zbl 0090.114)] for Chebyshev regression, which is therefore model-robust against uniform departures. The conditions also shed light on other classical results of Kiefer and Wolfowitz and of others.

### MSC:

62K05 | Optimal statistical designs |

62J02 | General nonlinear regression |

41A50 | Best approximation, Chebyshev systems |