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March, 1993 Minimax Regression Designs Under Uniform Departure Models
Dei-In Tang
Ann. Statist. 21(1): 434-446 (March, 1993). DOI: 10.1214/aos/1176349035


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 Kiefer and Wolfowitz for Chebyshev regression, which is therefore model-robust against uniform departure. The conditions also shed light on other classical results of Kiefer and Wolfowitz and of others.


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Dei-In Tang. "Minimax Regression Designs Under Uniform Departure Models." Ann. Statist. 21 (1) 434 - 446, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0773.62053
MathSciNet: MR1212186
Digital Object Identifier: 10.1214/aos/1176349035

Primary: 62K05
Secondary: 41A50, 62J02

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • March, 1993
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