Bayesian Quantile-on-Quantile Regression

Bayesian Quantile-on-Quantile (BQQ) Regression extends the Sim-Zhou quantile-on-quantile framework by replacing frequentist local linear estimation with Bayesian posterior inference. For each pair of quantiles (theta of the outcome, tau of the predictor), the method yields a full posterior distribution over the slope, enabling uncertainty quantification across the entire bivariate quantile surface — a key advantage when sample sizes are moderate and tail quantiles are sparse.