Precision of the path of steepest ascent in response surface methodology

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Sztendur, Ewa M (2005) Precision of the path of steepest ascent in response surface methodology. PhD thesis, Victoria University.

Abstract

This thesis provides some extensions to the existing method of determining the precision of the path of steepest ascent in response surface methodology to cover situations with correlated and heteroscedastic responses, including the important class of generalised linear models. It is shown how the eigenvalues of a certain matrix can be used to express the proportion of included directions in the confidence cone for the path of steepest ascent as an integral, which can then be computed using numerical integration. In addition, some tight inequalities for the proportion of included directions are derived for the two, three, and four dimensional cases. For generalised linear models, methods are developed using the Wald approach and profile likelihood confidence regions approach, and bootstrap methods are used to improve the accuracy of the calculations.

Item type Thesis (PhD thesis)
URI https://vuir.vu.edu.au/id/eprint/15792
Subjects Current > FOR Classification > 0104 Statistics
Historical > Faculty/School/Research Centre/Department > School of Engineering and Science
Current > FOR Classification > 0103 Numerical and Computational Mathematics
Keywords Response surfaces, statistics, linear models, eigenvalues, numerical integration, Wald approach, profile likelihood confidence regions, bootstrap methods
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