Bayesian analysis for quantile smoothing spline

ISSN 2475-4269

CN 31-2182/O1

Dongchu Sun

Faculty of Economics and Management, School of Statistics, East China Normal University, Shanghai, People’s Republic of China; Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE, USA

Pages 346-364 | Received 02 Jan. 2021, Accepted 18 Jun. 2021, Published online: 06 Jul. 2021,

Abstract
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In Bayesian quantile smoothing spline [Thompson, P., Cai, Y., Moyeed, R., Reeve, D., & Stander, J.(2010). Bayesian nonparametric quantile regression using splines. Computational Statistics andData Analysis, 54, 1138–1150.], a fixed-scale parameter in the asymmetric Laplace likelihoodtends to result in misleading fitted curves. To solve this problem, we propose a new Bayesianquantile 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 ofestimation accuracy and precision. Thirdly, NBQSS is robust to possible outliers and could provide accurate estimation.

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To cite this article: Zhongheng Cai & Dongchu Sun (2021) Bayesian analysis for
quantile smoothing spline, Statistical Theory and Related Fields, 5:4, 346-364, DOI:
10.1080/24754269.2021.1946372
To link to this article: https://doi.org/10.1080/24754269.2021.1946372

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