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

  • Duality
  • Nonparametric empirical Bayes

• Graduation date

  Fall 2014

• 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.