Bayesian semiparametric additive quantile regression
AbstractQuantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields posterior modes equivalent to frequentist estimates. In this paper, we utilize a location-scale-mixture of normals representation of the asymmetric Laplace distribution to transfer different flexible modeling concepts from Gaussian mean regression to Bayesian semiparametric quantile regression. In particular, we will consider high-dimensional geoadditive models comprising LASSO regularization priors and mixed models with potentially non-normal random effects distribution modeled via a Dirichlet process mixture. These extensions are illustrated using two large-scale applications on net rents in Munich and longitudinal measurements on obesity among children.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2012-06.
Date of creation: Apr 2012
Date of revision:
Contact details of provider:
Postal: Universitätsstraße 15, A - 6020 Innsbruck
Web page: http://www.uibk.ac.at/fakultaeten/volkswirtschaft_und_statistik/index.html.en
More information through EDIRC
asymmetric Laplace distribution; Bayesian quantile regression; Dirichlet process mixtures; LASSO; P-splines;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
- Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
- Roger Koenker & Ivan Mizera, 2004. "Penalized triograms: total variation regularization for bivariate smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 145-163.
- Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
- Yue, Yu Ryan & Rue, Håvard, 2011. "Bayesian inference for additive mixed quantile regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 84-96, January.
- Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
- Fenske, Nora & Kneib, Thomas & Hothorn, Torsten, 2011. "Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 494-510.
- Andreas Brezger & Thomas Kneib & Stefan Lang, . "BayesX: Analyzing Bayesian Structural Additive Regression Models," Journal of Statistical Software, American Statistical Association, vol. 14(i11).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Janette Walde).
If references are entirely missing, you can add them using this form.