BAYESIAN SPLINE REGRESSION ADAPTIVE FOR SEMIPARAMETRIC QUANTILE MODEL

Abstract

Quantile regression offers a powerful framework for analyzing the entire conditional distribution of a response variable, particularly in the presence of heterogeneous effects or non-standard error structures. While parametric approaches may lack flexibility and fully nonparametric methods often suffer from high variance, semiparametric models provide a useful compromise by combining interpretable parametric components with flexible nonparametric elements. In this paper, we propose a Bayesian Spline Semiparametric Quantile Regression (BSSQR) framework that employs adaptive Reversible Jump Markov Chain Monte Carlo (RJMCMC) to automatically determine both the number and locations of spline knots, thereby eliminating the need for manual tuning. The model is formulated hierarchically using an asymmetric Laplace likelihood, which facilitates simultaneous estimation of quantile functions and associated uncertainty. The performance of the proposed method is evaluated through extensive simulation studies and a real data application, demonstrating its effectiveness and practical advantages.