Robust Designs for Model Discrimination and Prediction of a Threshold Probability

  • Author / Creator
  • 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.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. 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.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • statistics
  • Supervisor / co-supervisor and their department(s)
    • Wiens, Douglas (Mathematical and Statistical sciences)
  • Examining committee members and their departments
    • Tsui, Ying (Electrical & Computer Engineering)
    • Notz, William (Department of Statistics, The Ohio State University)
    • Karunamuni, Rohana (Mathematical and Statistical sciences)
    • Wiens, Douglas (Mathematical and Statistical sciences)
    • Kong, Linglong (Mathematical and Statistical sciences)