Bayesian empirical likelihood for quantile regression

Yang, Yunwen

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

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

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

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

Copyright and License Information

Copyright 2011 Yunwen Yang

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