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August 2006 Optimal designs which are efficient for lack of fit tests
Wolfgang Bischoff, Frank Miller
Ann. Statist. 34(4): 2015-2025 (August 2006). DOI: 10.1214/009053606000000597

Abstract

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the linear model can be checked are accepted in practice. For important linear regression models such as polynomial regression, optimal designs do not have this property. To get practically attractive designs, we suggest the following strategy. One part of the design points is used to allow one to carry out a lack of fit test with good power for practically interesting alternatives. The rest of the design points are determined in such a way that the whole design is optimal for inference on the unknown parameter in case the lack of fit test does not reject the linear regression model.

To solve this problem, we introduce efficient lack of fit designs. Then we explicitly determine the ek-optimal design in the class of efficient lack of fit designs for polynomial regression of degree k−1.

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Wolfgang Bischoff. Frank Miller. "Optimal designs which are efficient for lack of fit tests." Ann. Statist. 34 (4) 2015 - 2025, August 2006. https://doi.org/10.1214/009053606000000597

Information

Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.62175
MathSciNet: MR2283725
Digital Object Identifier: 10.1214/009053606000000597

Subjects:
Primary: 62F05 , 62J05
Secondary: 62F05

Keywords: efficient maximin power , Linear regression models , optimal designs to estimate the highest coefficient , polynomial regression of degree k−1 , testing lack of fit

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 4 • August 2006
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