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Robust regression designs for approximate polynomial models. (English) Zbl 1021.62058
Summary: We consider robust designs for approximate polynomial regression models, by applying the theory of canonical moments. The design criterion, first given by S. X. Liu and D. P. Wiens [J. Stat. Plann. Inference 64, 369-381 (1997; Zbl 0946.62068)], is to maximize the determinant of the information matrix subject to a side condition of bounding the bias arising from model misspecification. We give a new proof of, and extend, the main theorem of Liu and Wiens (op. cit.); in so doing we shed new light on the structure of this problem. New designs, with the further property of minimizing the generalized variance of the additional regression coefficients when an enlarged model is fitted, are derived and assessed. These provide additional robustness against uncertainty regarding the proper degree of the fitted polynomial response.

MSC:
62K25 Robust parameter designs
62J02 General nonlinear regression
62J05 Linear regression; mixed models
62K05 Optimal statistical designs
62F35 Robustness and adaptive procedures (parametric inference)
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