Regression Adjustment for Noncrossing Bayesian Quantile Regression

ABSTRACT

A two-stage approach is proposed to overcome the problem in quantile regression, where separately fitted curves for several quantiles may cross. The standard Bayesian quantile regression model is applied in the first stage, followed by a Gaussian process regression adjustment, which monotonizes the quantile function while borrowing strength from nearby quantiles. The two-stage approach is computationally efficient, and more general than existing techniques. The method is shown to be competitive with alternative approaches via its performance in simulated examples. Supplementary materials for the article are available online.

KEYWORDS:

• Asymmetric Laplace distribution
• Crossing quantile regression
• Gaussian process regression
• Monotonicity

Supplementary Materials

Codes and datasets: The supplemental files include R codes to perform the two-stage approach (GPreg.R) and datasets used as examples (igg.dta, sl_ns_global.txt).

Acknowledgments

The first author is funded by CAPES Foundation via the Science Without Borders (BEX 0979/13-9).