Robustness of A-optimal designs

摘要

Suppose that Y = (Y-i) is a normal random vector with mean Xb and covariance sigma(2)l(n) where h is a p-dimensional vector (b(j)), X = (X-ij) is an n x p matrix. A-optimal designs X are chosen from the traditional set 9 of A-optimal designs for p = 0 such that X is still A-optimal in D when the components Yi are dependent, i.e., for i not equal i', the covariance of Y-i, Y-i, is rho with rho not equal 0. Such designs depend on the sign of rho. The general results are applied to X = (X-ij), where X-ij epsilon {-1, 1}; this corresponds to a factorial design with -1, 1 representing low level or high level respectively, or corresponds to a weighing design with -1, 1 representing an object j with weight b(j) being weighed on the left and right of a chemical balance, respectively. (C) 2008 Elsevier Inc. All rights reserved.