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December, 1984 Some Model Robust Designs in Regression
Jerome Sacks, Donald Ylvisaker
Ann. Statist. 12(4): 1324-1348 (December, 1984). DOI: 10.1214/aos/1176346795


Theory for finding designs in estimating a linear functional of a regression function is developed for classes of regression functions which are infinite dimensional. These classes can be viewed as representing possible departures from an "ideal" simple model and thus describe a model robust setting. The estimates are restricted to be linear and the design (and estimate) sought is minimax for mean square error. The structure of the design is obtained in a variety of cases; some asymptotic theory is given when the functionals are integrals. As to be expected, optimal designs depend critically on the particular functional to be estimated. The associated estimate is generally not a least squares estimate but we note some examples where a least squares estimate, in conjunction with a good design, is adequate.


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Jerome Sacks. Donald Ylvisaker. "Some Model Robust Designs in Regression." Ann. Statist. 12 (4) 1324 - 1348, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0556.62054
MathSciNet: MR760692
Digital Object Identifier: 10.1214/aos/1176346795

Primary: 62K05
Secondary: 62J02

Keywords: approximately linear models , linear estimation , minimax designs , model robustness , Nonparametric regression , optimal design , regression design

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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