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)

  • Subjects / Keywords
  • Graduation date
    Fall 2014
  • Type of Item
  • Degree
    Master of Science
  • 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.