Bayesian analysis for quantile smoothing spline. Issue 4 (2nd October 2021)

• Record Type: Journal Article
• Authors: Cai, Zhongheng; Sun, Dongchu
• Is Part Of: Statistical theory and related fields. Volume 5:Issue 4(2021)
• Page Start: 346
• Page End: 364
• Publication Date: 2021-10-02
• Subjects: asymmetric Laplace likelihood -- objective Bayesian analysis -- posterior propriety -- quantile regression -- smoothing spline; Statistics -- Periodicals; Statistics; Periodicals; Electronic journals; 001.422
• DOI: 10.1080/24754269.2021.1946372
• Languages: English
• ISSNs: 2475-4269

Abstract

Abstract : In Bayesian quantile smoothing spline [Thompson, P., Cai, Y., Moyeed, R., Reeve, D., & Stander, J. (2010). Bayesian nonparametric quantile regression using splines. Computational Statistics and Data Analysis, 54, 1138–1150.], a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves. To solve this problem, we propose a new Bayesian quantile smoothing spline (NBQSS), which considers a random scale parameter. To begin with, we justify its objective prior options by establishing one sufficient and one necessary condition of the posterior propriety under two classes of general priors including the invariant prior for the scale component. We then develop partially collapsed Gibbs sampling to facilitate the computation. Out of a practical concern, we extend the theoretical results to NBQSS with unobserved knots. Finally, simulation studies and two real data analyses reveal three main findings. Firstly, NBQSS usually outperforms other competing curve fitting methods. Secondly, NBQSS considering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision. Thirdly, NBQSS is robust to possible outliers and could provide accurate estimation.