Open Access
March 2012 Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach
Surya T. Tokdar, Joseph B. Kadane
Bayesian Anal. 7(1): 51-72 (March 2012). DOI: 10.1214/12-BA702


We introduce a semi-parametric Bayesian framework for a simultaneous analysis of linear quantile regression models. A simultaneous analysis is essential to attain the true potential of the quantile regression framework, but is computationally challenging due to the associated monotonicity constraint on the quantile curves. For a univariate covariate, we present a simpler equivalent characterization of the monotonicity constraint through an interpolation of two monotone curves. The resulting formulation leads to a tractable likelihood function and is embedded within a Bayesian framework where the two monotone curves are modeled via logistic transformations of a smooth Gaussian process. A multivariate extension is suggested by combining the full support univariate model with a linear projection of the predictors. The resulting single-index model remains easy to fit and provides substantial and measurable improvement over the first order linear heteroscedastic model. Two illustrative applications of the proposed method are provided.


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Surya T. Tokdar. Joseph B. Kadane. "Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach." Bayesian Anal. 7 (1) 51 - 72, March 2012.


Published: March 2012
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62193
MathSciNet: MR2896712
Digital Object Identifier: 10.1214/12-BA702

Keywords: Bayesian inference , Bayesian nonparametric models , Gaussian processes , Joint Quantile Model , Linear Quantile Regression , Monotone Curves

Rights: Copyright © 2012 International Society for Bayesian Analysis

Vol.7 • No. 1 • March 2012
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