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Permanent link (DOI): https://doi.org/10.7939/R3RX93N43

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Convex Duality in Nonparametric Empirical Bayes Estimation and Prediction Open Access

Descriptions

Other title
Subject/Keyword
nonparametric empirical Bayes
duality
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Tao, Sile
Supervisor and department
Mizera, Ivan (Mathematical and Statistical Sciences)
Examining committee member and department
Choulli, Tahir (Mathematical and Statistical Sciences)
Prasad, Narasimha (Mathematical and Statistical Sciences)
Gombay, Edit (Mathematical and Statistical Sciences)
Mizera, Ivan (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Statistics
Date accepted
2014-06-17T10:48:24Z
Graduation date
2014-11
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3RX93N43
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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