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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/37246 |
| Date | 01 February 2006 |
| Creators | Baran, Gary Steven |
| Contributors | Statistics, Myers, Raymond H., Foutz, Robert, Smith, Eric P., Reynolds, Marion R. Jr., Terrell, George R. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | ix, 116 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 27379460, LD5655.V856_1992.B373.pdf |
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