Locally Optimal Designs for Binary and Weighted Regression Models

Musrati, Abdelmagid K (1992) Locally Optimal Designs for Binary and Weighted Regression Models. MSc(R) thesis, University of Glasgow.

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Abstract

The main aim of this thesis is to review and augment the theory and methods of optimal experimental designs for non-linear problems with a single variable using geometric and other arguments. It represents a continuation of the work on locally optimal designs for binary response experiments, which has been studied by Ford, Torsney, and Wu (1992) among others. Chapter 1 serves as an introduction to the non-linear design problem. The main point of difference between the non-linear case is emphasised and contrasted with the linear case. Chapter 2 presents a review of the general theory and the appropriate notation needed for the development of this thesis. Also the canonical transformation of a design problem is discussed. A necessary and sufficient condition for D-optimality of a design measure is given. Chapters 3 and 4 are devoted to the problem of constructing locally D- optimal and c-optimal designs for two parameter models respectively. In addition, the geometrical characterisation of designs optimising these criteria is discussed. Explicit solutions to compute the optimal weights of such designs are derived. Several examples of optimal designs which may be found analytically are given in chapter 3. In chapter 5 attention is focused on the problem of determining D-optimal designs for three parameter models, including those for weighted quadratic regression and generalised linear models. Chapter 6, considering the situations and problems for future work, gives a list of possible ways in which the work of this thesis may be extended.

Item Type: Thesis (MSc(R))
Qualification Level: Masters
Additional Information: Adviser: Ben Torsney
Keywords: Statistics
Date of Award: 1992
Depositing User: Enlighten Team
Unique ID: glathesis:1992-76417
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Nov 2019 14:32
Last Modified: 19 Nov 2019 14:32
URI: http://theses.gla.ac.uk/id/eprint/76417

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