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Permanent link (DOI): https://doi.org/10.7939/R3W121

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Designs for nonlinear regression with a prior on the parameters Open Access

Descriptions

Other title
Subject/Keyword
nonlinear regression
mutation
genetic algorithm
GA
robustness
minimax design
crossover
designs
information matrix
loss function
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Karami, Jamil
Supervisor and department
Wiens, Doug (Mathematical and Statistical Sciences)
Examining committee member and department
Li, Pengfei (Mathematical and Statistical Sciences)
Schmuland, Byron (Mathematical and Statistical Sciences)
Heo, Giseon (Dentistry and Pharmacy)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-09-07T16:55:37Z
Graduation date
2011-11
Degree
Master of Science
Degree level
Master's
Abstract
This thesis deals with finding design points for nonlinear regression models with the possibility that the fitted model is incorrect. The information matrix depends on the parameter in nonlinear situations. We have assumed a range of values of the parameter and have specified a prior on the parameter space. A loss function has been developed and then a minimax approach has been adopted to achieve our goal. We have found an explicit expression for the maximized loss and a numerical minimization of it has been done by a genetic algorithm (GA). The whole approach has been implemented by considering some well-known nonlinear functions. We see that changing the values of the parameter of the prior density have effect on design points. However, changing the tuning constants of GA does not alter the design points noticeably. This indicates that we have obtained the minimizing design.
Language
English
DOI
doi:10.7939/R3W121
Rights
License granted by Jamil Karami (mdjamilh@ualberta.ca) on 2011-09-04T04:50:41Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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