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Exact optimal designs for weighted least squares analysis with correlated errors. (English) Zbl 1137.62046

Summary: In the common linear and quadratic regression model with an autoregressive error structure exact \(D\)-optimal designs for weighted least squares analysis are determined. It is demonstrated that for highly correlated observations the \(D\)-optimal design is close to the equally spaced design. Moreover, the equally spaced design is usually very efficient, even for moderate sizes of the correlation, while the \(D\)-optimal design obtained under the assumptions of independent observations yields a substantial loss in efficiency. We also consider the problem of designing experiments for weighted least squares estimation of the slope in a linear regression and compare the exact \(D\)-optimal designs for weighted and ordinary least squares analysis.

MSC:

62K05 Optimal statistical designs
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
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