Bayesian semiparametric additive quantile regression
By Elisabeth Waldmann, Thomas Kneib, Y. Yue, Stefan Lang, C. Flexeder. 2013
125 citations recorded by the source corpus.
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 modelling 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. The impact of the likelihood misspecification that underlies the Bayesian formulation of quantile regression is studied in terms of simulations.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/7f861667c6c9bc824305f2e4df242bcba182cdec
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In Artificial Intelligence
- Thomas Kneib
- Elisabeth Waldmann
- Simon N. Wood
- Margaux Zaffran
- Yannig Goude
- Raphael Nedellec
- Matteo Fasiolo
In Statistics and Probability
- Thomas Kneib
- Yannig Goude
- Margaux Zaffran
- Raphael Nedellec
- Matteo Fasiolo
- Elisabeth Waldmann
- Simon N. Wood
- Stefan Lang
Citations in the corpus
- Fast Calibrated Additive Quantile Regression (2017, methodology): “on, mboost uses bootstrapping to estimate parameter uncertainty, while the approach proposed here quantifies uncertainty using computationally efficient asymptotic approximations. Yue and Rue (2011) and Waldmann et al. (2013) describe how to perform Bayesian inference for semi-parametric additive quant”
- Quantile regression: A short story on how and why (2018, background): “Uncertainty can hence be captured approximately, but variances of parameters are usually underestimated (Waldmann et al., 2013).”
- Beyond mean regression (2013, methodology): “This problem is investigated in more detail in Waldmann et al. (2013) who study Bayesian quantile regression in simulations and complex case studies and also compare the results with those from a frequentist analysis using quantile smoothing splines (Koenker et al., 1994).”