Simultaneous fitting of Bayesian penalised quantile splines

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. The pyramid quantile regression method for simultaneous linear quantile fitting is adapted for the spline regression setting. In high dimensional problems, the choice of the pyramid locations becomes crucial for a robust parameter estimation. The optimal pyramid locations are derived which then allows for an efficient adaptive block-update MCMC scheme to be proposed for posterior computation. Simulation studies show that the proposed method provides estimates with significantly smaller errors and better empirical coverage probability when compared to existing alternative approaches. The method is illustrated with three real applications.

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