Estimating main effects with pareto optimal subsets
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Abstract
A subset T of S is said to be a Pareto Optimal Subset of m ordered attributes (factors) if for profiles (combination of attribute levels) (x<sub>1</sub>, x<sub>2</sub>, .... x<sub>m</sub>) and (y<sub>1</sub>, y<sub>2</sub>, .... y<sub>m</sub>) ∈ T, no profile "dominates" another; that is, there exist no pair such that x<sub>1</sub> ≤ y<sub>1</sub>, for i = 1, 2, .... m. The experimental design problem here is to select a Pareto Optimal subset, or subsets, such that we can estimate all elementary contrasts between the levels of each attribute of a main-effects design
