Exact optimal designs for weighted least squares analysis with correlated errors
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Date
2006-02-10T11:11:06Z
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Abstract
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.
AMS Subject Classification: 62K05
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Keywords
Autoregressive errors, Estimation of the slope, Exact D-optimal designs, Generalized MANOVA, Linear regression, Quadratic regression