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Convex Duality in Nonparametric Empirical Bayes Estimation and Prediction

  • Author / Creator
    Tao, Sile
  • The primary goal of this thesis is to implement the Kiefer-Wolfowitz nonparametric empirical Bayes method for models with multivariate response, using the idea of the dual algorithm outlined in a paragraph from Koenker and Mizera (2014). The approach of Kiefer-Wolfowitz was numerically elaborated by Koenker and Mizera (2014) and applied to the univariate normal means problem. For the problems with multivariate response, their method may be not numerically feasible. If the dual problem is considered instead, we are able to come up with an adaptive algorithm, which iteratively uses unequally spaced grids to approximate the prior. In this way, we can solve the dual problem without using overly many grid points. Another objective of the thesis is to facilitate the multivariate data-analytic application of the developed algorithm. To this end, we study Tweedie's formula, which can be used to compute the posterior mean, after the estimate of the prior is obtained. Finally, the formulation of the Koenker-Mizera dual has been justified in the discretized setting as the Lagrange dual of the original (discretized) formulation.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3RX93N43
  • 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
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistics
  • Supervisor / co-supervisor and their department(s)
    • Mizera, Ivan (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Mizera, Ivan (Mathematical and Statistical Sciences)
    • Prasad, Narasimha (Mathematical and Statistical Sciences)
    • Choulli, Tahir (Mathematical and Statistical Sciences)
    • Gombay, Edit (Mathematical and Statistical Sciences)