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Robust Designs for Model Discrimination and Prediction of a Threshold Probability Open Access


Other title
robust designs
model discrimination
threshold probability
Type of item
Degree grantor
University of Alberta
Author or creator
Supervisor and department
Wiens, Douglas (Mathematical and Statistical sciences)
Examining committee member and department
Karunamuni, Rohana (Mathematical and Statistical sciences)
Kong, Linglong (Mathematical and Statistical sciences)
Wiens, Douglas (Mathematical and Statistical sciences)
Tsui, Ying (Electrical & Computer Engineering)
Notz, William (Department of Statistics, The Ohio State University)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
2016-06:Fall 2016
Doctor of Philosophy
Degree level
Robust Designs for Model Discrimination and Prediction of a Threshold Probability” In the first of the two projects comprising this thesis we consider the construction of experimental designs aimed at the elucidation of a functional relationship between a response variable and various covariates, under various forms of model uncertainty. In such a scenario a central goal may be to design in order to distinguish between rival models. Usually, one can cast the model discrimination problem as one of hypothesis testing. From a point view of robustness it is realistic to suppose that the correct model lies in one of those only approximately known classes centered on those rival models. Under the assumption that the true model is in a Hellinger neighbourhood of one of the nominal models, we propose methods of construction for experimental designs by maximizing the worst power of the NeymanPearson test over the Hellinger neighbourhoods. The asymptotic properties of the NeymanPearson test statistic is derived. The optimal designs are ''maximin" designs, which maximize (through the design) the minimum (among the neighbourhoods) asymptotic power function. To motivate the second project, we note that stochastic processes are widely used in the study of phenomena nowadays. Usually, for a model used to describe the observed data of the stochastic process, people are interested in estimating the threshold probability that the deterministic mean perturbed by stochastic errors at each location is above a fixed threshold. We consider methods for the construction of robust sampling designs for the estimation of the threshold probability, with particular attention being paid to the effect of spatial correlation between adjoining locations and the regression response functions. A ''minimax'' approach is adopted. The optimal design minimizes the maximum over the neighbourhood of the working model of the loss function.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
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