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Statistica Sinica 21 (2011), 421-432





OPTIMALITY CRITERIA FOR MULTIRESPONSE

LINEAR MODELS BASED ON PREDICTIVE ELLIPSOIDS


Xin Liu$^{1,2}$, Rong-Xian Yue$^{1,3}$ and Fred J. Hickernell$^4$


$^1$Shanghai Normal University, $^2$Donghua University,
$^3$E-Institute of Shanghai Universities and $^4$Illinois Institute of Technology


Abstract: This paper proposes a new class of optimum design criteria for the linear regression model with $r$ responses based on the volume of the predictive ellipsoid. This is referred to as $I_L^r$-optimality. The $I_L^r$-optimality criterion is invariant with respect to different parameterizations of the model, and reduces to $I_L$-optimality as proposed by Dette and O'brien (1999) in single response situations. An equivalence theorem for $I_L^r$-optimality is provided and used to verify $I_L^r$-optimality of designs, and this is illustrated by several examples.



Key words and phrases: General equivalence theorem, multiresponse linear models, optimal design, predictive ellipsoid.

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