Abstract
Suppose that Y = ( Y i ) is a normal random vector with mean Xb and covariance σ 2 I n , where b is a p -dimensional vector ( b j ) , X = ( X ij ) is an n × p matrix. A -optimal designs X are chosen from the traditional set D of A -optimal designs for ρ = 0 such that X is still A -optimal in D when the components Y i are dependent, i.e., for i ≠ i ′ , the covariance of Y i , Y i ′ is ρ with ρ ≠ 0 . Such designs depend on the sign of ρ . The general results are applied to X = ( X ij ) , where X ij ∈ { - 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.
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