Noncrossing simultaneous Bayesian quantile curve fitting

TL;DR

This paper introduces an adaptive pyramid quantile regression method for Bayesian noncrossing quantile curve estimation, improving accuracy and coverage in high-dimensional spline regression settings.

Contribution

It derives optimal pyramid locations and proposes an efficient MCMC scheme, advancing Bayesian quantile curve fitting with noncrossing constraints.

Findings

Smaller estimation errors compared to existing methods

Better empirical coverage probabilities

Effective in high-dimensional problems

Abstract

Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. This paper presents the use of the pyramid quantile regression method in the spline regression setting. In high dimensional problems, the choice of the pyramid locations becomes crucial for a robust parameter estimation. In this work we derive the optimal {pyramid locations which then allows us to propose an efficient} adaptive block-update MCMC scheme for posterior computation. Simulation studies show the proposed method provides estimates with significantly smaller errors and better empirical coverage probability when compared to existing alternative approaches. We illustrate the method with three real applications.