Bayesian semiparametric additive quantile regression
Quantile 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.
|Date of creation:||Apr 2012|
|Date of revision:|
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- Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
- 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.
- 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.
- 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.
- 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.
- Brezger, Andreas & Kneib, Thomas & Lang, Stefan, 2005. "BayesX: Analyzing Bayesian Structural Additive Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i11).
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