Bayesian analysis for quantile smoothing spline
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2021-10-01
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| Series: | Statistical Theory and Related Fields |
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| Online Access: | http://dx.doi.org/10.1080/24754269.2021.1946372 |
| _version_ | 1797677033543696384 |
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| author | Zhongheng Cai Dongchu Sun |
| author_facet | Zhongheng Cai Dongchu Sun |
| author_sort | Zhongheng Cai |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T22:39:03Z |
| format | Article |
| id | doaj.art-b91a7c4764cb430b9fc18306b785fe70 |
| institution | Directory Open Access Journal |
| issn | 2475-4269 2475-4277 |
| language | English |
| last_indexed | 2024-03-11T22:39:03Z |
| publishDate | 2021-10-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Statistical Theory and Related Fields |
| spelling | doaj.art-b91a7c4764cb430b9fc18306b785fe702023-09-22T09:19:46ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772021-10-015434636410.1080/24754269.2021.19463721946372Bayesian analysis for quantile smoothing splineZhongheng Cai0Dongchu Sun1Faculty of Economics and Management, School of Statistics, East China Normal UniversityFaculty of Economics and Management, School of Statistics, East China Normal UniversityIn 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.http://dx.doi.org/10.1080/24754269.2021.1946372asymmetric laplace likelihoodobjective bayesian analysisposterior proprietyquantile regressionsmoothing spline |
| spellingShingle | Zhongheng Cai Dongchu Sun Bayesian analysis for quantile smoothing spline Statistical Theory and Related Fields asymmetric laplace likelihood objective bayesian analysis posterior propriety quantile regression smoothing spline |
| title | Bayesian analysis for quantile smoothing spline |
| title_full | Bayesian analysis for quantile smoothing spline |
| title_fullStr | Bayesian analysis for quantile smoothing spline |
| title_full_unstemmed | Bayesian analysis for quantile smoothing spline |
| title_short | Bayesian analysis for quantile smoothing spline |
| title_sort | bayesian analysis for quantile smoothing spline |
| topic | asymmetric laplace likelihood objective bayesian analysis posterior propriety quantile regression smoothing spline |
| url | http://dx.doi.org/10.1080/24754269.2021.1946372 |
| work_keys_str_mv | AT zhonghengcai bayesiananalysisforquantilesmoothingspline AT dongchusun bayesiananalysisforquantilesmoothingspline |