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The Expectation–Maximization approach for Bayesian quantile regression

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  • Zhao, Kaifeng
  • Lian, Heng

Abstract

This paper deals with Bayesian linear quantile regression models based on a recently developed Expectation–Maximization Variable Selection (EMVS) method. By using additional latent variables, the proposed approach enjoys enormous computational savings compared to commonly used Markov Chain Monte Carlo (MCMC) algorithm. Using location-scale mixture representation of asymmetric Laplace distribution (ALD), we develop a rapid and efficient Expectation–Maximization (EM) algorithm, which is illustrated with several carefully designed simulation examples. We further apply the proposed method to construct financial index tracking portfolios.

Suggested Citation

  • Zhao, Kaifeng & Lian, Heng, 2016. "The Expectation–Maximization approach for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 1-11.
    • Handle: RePEc:eee:csdana:v:96:y:2016:i:c:p:1-11
    DOI: 10.1016/j.csda.2015.11.005
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    References listed on IDEAS

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    1. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    2. Veronika Ročková & Edward I. George, 2014. "EMVS: The EM Approach to Bayesian Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 828-846, June.
    3. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    4. G. Yi & J. Q. Shi & T. Choi, 2011. "Penalized Gaussian Process Regression and Classification for High-Dimensional Nonlinear Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1285-1294, December.
    5. R. Alhamzawi & K. Yu & D. F. Benoit, 2011. "Bayesian adaptive Lasso quantile regression," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 11/728, Ghent University, Faculty of Economics and Business Administration.
    6. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    7. Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    8. Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
    9. Li, Fan & Zhang, Nancy R., 2010. "Bayesian Variable Selection in Structured High-Dimensional Covariate Spaces With Applications in Genomics," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1202-1214.
    10. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    11. Reich, Brian J. & Fuentes, Montserrat & Dunson, David B., 2011. "Bayesian Spatial Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 6-20.
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    Cited by:

    1. Julio Cezar Soares Silva & Adiel Teixeira de Almeida Filho, 2023. "A systematic literature review on solution approaches for the index tracking problem in the last decade," Papers 2306.01660, arXiv.org, revised Jun 2023.
    2. Matthew D. Koslovsky & Michael D. Swartz & Wenyaw Chan & Luis Leon†Novelo & Anna V. Wilkinson & Darla E. Kendzor & Michael S. Businelle, 2018. "Bayesian variable selection for multistate Markov models with interval†censored data in an ecological momentary assessment study of smoking cessation," Biometrics, The International Biometric Society, vol. 74(2), pages 636-644, June.

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