Improved Design Criteria Robust for Complex Variance Structures

UoM administered thesis: Phd

  • Authors:
  • Camilla Sammut-Powell

Abstract

There are many design criteria available which have been constructed to address specific statistical design problems. Although much research has been conducted to improve the design procedure to address the needs of the experiment, often with the introduction of new criteria, it can be that they lack robustness to assumptions meaning that the optimum design produced could be of little use if the experimental assumptions are not met. Not evaluating the robustness for such criteria could therefore be detrimental to a study and criteria which are highly sensitive to such issues should not be used. Within the thesis, we consider the performance of some chosen criteria for response surface studies when assumptions are no longer met. We demonstrate flaws in well accepted criteria and introduce new and improved criteria which are more appropriate for the construction and evaluation of designs. The problems addressed are for designs with interest in estimating the parameters and hence take some functional form of the D-optimality criterion. The new criteria proposed provide superior alternative designs to the naively constructed designs using the accepted criteria. The focus is on three problems: the effect of trends on designs, self-robustness of a design with respect to parameter estimates and the inappropriate use of a criterion developed from asymptotic results in small samples. The effect of trends has only been studied within a restrictive choice of models, with the aim of orthogonalizing the fixed effect parameters to the trend parameters. We propose a new criterion which allows the trend to affect the variance and for the response to have a non-normal distribution, as well as having other advantageous properties. We also propose a criterion to evaluate the self-robustness of a design, i.e. robust for the assumed parameter values, which uses the information matrix to generate the possibilities for the parameter estimate and is therefore dependent on the design. This is a dynamic approach and allows for an intrinsic assessment of the performance of a design. The inappropriate use of criteria developed from asymptotic results in small samples is our final design problem of interest. We propose using a corrected criterion, adjusting for the use of an asymptotic result in a small sample. The correction takes into account the use of the estimates of variance components and combines the information for the fixed effects and the variance components in a new way other than simply taking the product of the information matrices.

Details

Original languageEnglish
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Supervisors/Advisors
Award date1 Aug 2018