Bayesian Analysis

Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach

Joseph B. Kadane and Surya T. Tokdar

Full-text: Open access

Abstract

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.

Article information

Source
Bayesian Anal., Volume 7, Number 1 (2012), 51-72.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339616725

Digital Object Identifier
doi:10.1214/12-BA702

Mathematical Reviews number (MathSciNet)
MR2896712

Zentralblatt MATH identifier
1330.62193

Keywords
Bayesian Inference Bayesian Nonparametric Models Gaussian Processes Joint Quantile Model Linear Quantile Regression Monotone Curves

Citation

Tokdar, Surya T.; Kadane, Joseph B. Simultaneous Linear Quantile Regression: A Semiparametric Bayesian Approach. Bayesian Anal. 7 (2012), no. 1, 51--72. doi:10.1214/12-BA702. https://projecteuclid.org/euclid.ba/1339616725


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