Statistica Sinica 18(2008), 135-154

EXACT OPTIMAL DESIGNS FOR WEIGHTED LEAST

SQUARES ANALYSIS WITH CORRELATED ERRORS

Holger Dette, Joachim Kunert and Andrey Pepelyshev

Ruhr-Universität Bochum, Universität Dortmund

and St. Petersburg State University

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.