Simultaneous linear quantile regression: A semiparametric bayesian approach

Journal Article

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 computa-tionally 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 lo-gistic 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. © 2012 International Society for Bayesian Analysis.

Full Text

Duke Authors

Cited Authors

  • Tokdar, ST; Kadaney, JB

Published Date

  • 2012

Published In

Volume / Issue

  • 7 / 1

Start / End Page

  • 51 - 72

International Standard Serial Number (ISSN)

  • 1936-0975

Digital Object Identifier (DOI)

  • 10.1214/12-BA702