Bayesian non-crossing quantile regression for regularly varying distributions

ABSTRACT

Quantile regression is a very important statistical tool for predictive modelling and risk assessment. For many applications, conditional quantile at different levels are estimated separately. Consequently the monotonicity of conditional quantiles can be violated when quantile regression curves cross each other. In this paper, we propose a new Bayesian multiple quantile regression based on heavy tailed distribution for non-crossing. We consider a linear quantile regression model for simultaneous Bayesian estimation of multiple quantiles based on a regularly varying assumptions. The numerical and competitive performance of the proposed method is illustrated by simulation.

KEYWORDS:

• Quantile regression
• non-crossing curves
• regularly varying distributions
• heavy tailed behaviour
• conditional quantile curves

Acknowledgements

The Author thanks the Editor in chief, the reviewers for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) [RGPIN-2014-04029].