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A two-stage experimental design procedure under dispersion effectsBaran, Gary Steven 01 February 2006 (has links)
Under heterogeneous variance, conventional optimal response surface experimental designs for estimating location models are no longer optimal. To address this deficiency. D and Q criteria appropriate under heterogeneous variance are developed. These criteria are then applied to demonstrate the improved efficiency of a proposed two-stage experimental design procedure. In the proposed procedure the first stage estimates the heterogeneous variance structure and the second stage augments the first stage to produce a total design that is Q or D-optimal for the estimated variance structure. The Q and 0 criteria not only direct the total design, but also suggest optimal designs for estimating dispersion effects in the first stage.
The efficiency of the proposed two-stage procedure is further enhanced if certain mild assumptions concerning variance structure are valid. These assumptions are formulated as a prior distribution and effectively stabilize the variance estimation in the first stage through a Bayes estimator. / Ph. D.
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