University of Illinois Urbana-Champaign

Bayesian empirical likelihood for quantile regression

Yang, Yunwen

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Yang_Yunwen.pdf

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https://hdl.handle.net/2142/29522

Description

Title
Bayesian empirical likelihood for quantile regression
Author(s)
Yang, Yunwen
Issue Date
2012-02-01T00:53:52Z
Director of Research (if dissertation) or Advisor (if thesis)
He, Xuming
Doctoral Committee Chair(s)
He, Xuming
Committee Member(s)
  • Chen, Yuguo
  • Koenker, Roger W.
  • Portnoy, Stephen L.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2012-02-01T00:53:52Z
Keyword(s)
  • Efficiency
  • Empirical likelihood
  • High quantiles
  • Quantile regression
  • Prior
  • Posterior.
Abstract
Bayesian inference provides a flexible way of combiningg data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigations. This thesis considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior is asymptotically normal; its mean shrinks towards the true parameter values and its variance approaches that of the maximum empirical likelihood estimator. Through empirical likelihood, the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains in the estimation of multiple quantiles. By using an MCMC algorithm in the computation, we avoid the daunting task of directly maximizing empirical likelihoods. The finite sample performance of the proposed method is investigated empirically, where substantial efficiency gains are demonstrated with informative priors on common features across quantile levels.
Graduation Semester
2011-12
Permalink
http://hdl.handle.net/2142/29522
Copyright and License Information
Copyright 2011 Yunwen Yang

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