收稿日期: 2019-03-06
网络出版日期: 2021-02-28
基金资助
国家自然科学基金资助项目(11471208)
Bayesian inference for semiparametric ordinal regression
Received date: 2019-03-06
Online published: 2021-02-28
赵焕丽, 何幼桦 . 半参数顺序回归的贝叶斯推断[J]. 上海大学学报(自然科学版), 2021 , 27(1) : 218 -226 . DOI: 10.12066/j.issn.1007-2861.2124
This study combines the proportional odds and semiparametric regression models to establish a general form of a semiparametric ordinal regression model. For the parametric and nonparametric parts of the model, a Bayesian estimator based on the finite dimensional distribution of the stochastic process is constructed, and the analytical expression of the estimator is given under normal conditions. Numerical simulation results reveal that, even in the case of small samples, the estimated values of the model parameters are close to the true values, and the estimated values of the non-parametric parts can describe the shape of the real function. An empirical analysis of predicted income levels based on household consumption structures shows that a difference exists in the consumption structures between urban residents and rural households at the same income level, and a better performance under extrapolation is identified.
| [1] | Cox D R. The analysis of multivariate binary data[J]. Journal of the Royal Statistical Society. Series C: Applied Statistics, 1972,21(2):113-120. |
| [2] | McCullagh P. Regression models for ordinal data[J]. Journal of the Royal Statistical Society. Series B: Methodological, 1980,42(2):109-127. |
| [3] | 熊笛, 何幼桦. 半参数顺序变量回归模型[J]. 上海大学学报(自然科学版), 2016,22(4):477-485. |
| [3] | Xiong D, He Y H. Semi-parametric ordinal variable regression model[J]. Journal of Shanghai University (Natural Science Edition), 2016,22(4):477-485. |
| [4] | Engle R, Granger C W J, Rice J, et al. Semiparametric estimates of the relation between weather and electricity sales[J]. Publications of the American Statistical Association, 1986,81(394):11. |
| [5] | 朱丹丹. 半参数回归模型的$k$-$d$ 估计[D]. 黄石: 湖北师范学院, 2012. |
| [5] | Zhu D D. The $k$-$d$ estimation in the semi-parametric regression model[D]. Huangshi: Hubei Normal University, 2012. |
| [6] | 郭兴翠. 半参数回归模型的估计方法和模拟分析[D]. 长沙: 中南大学, 2007. |
| [6] | Guo X C. Estimation method and simulation analysis of semi-parametric regression model[D]. Changsha: Central South University, 2007. |
| [7] | 靳坤坤. 半参数回归模型有偏估计的研究[D]. 北京: 中央民族大学, 2016. |
| [7] | Jin K K. Research on partial estimation of semi-parametric regression model[D]. Beijing: Minzu University of China, 2016. |
| [8] | Koop G, Poirer D J. Bayesian variants of some classical semiparametric regression techniques[J]. Journal of Econometrics, 2004,123(2):259-282. |
| [9] | Koop G, Tobias J L. Semiparametric Bayesian inference in smooth coefficient models[J]. Journal of Econometrics, 2006,134(1):283-315. |
| [10] | 李琪琪. 半参数回归模型的 Bayes 估计[D]. 合肥: 中国科学技术大学, 2009. |
| [10] | Li Q Q. Bayes estimation of semi-parametric regression model[D]. Hefei: University of Science and Technology of China, 2009. |
| [11] | Dimitrakopoulos S. Semiparametric Bayesian inference for time-varying parameter regression models with stochastic volatility[J]. Economics Letters, 2017,150:10-14. |
| [12] | Chow S M, Tang N, Yuan Y, et al. Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior[J]. British Journal of Mathematical & Statistical Psychology, 2011,64(1):69-106. |
| [13] | Kim I, Pang H, Zhao H. Bayesian semiparametric regression models for evaluating pathway effects on continuous and binary clinical outcomes[J]. Statistics in Medicine, 2012,31(15):1633-1651. |
| [14] | 茆诗松, 王静龙, 史定华, 等. 统计手册[M]. 北京: 科学出版社, 2003: 350-370. |
| [14] | Mao S S, Wang J L, Shi D H, et al. Statistics manual [M]. Beijing: Science Press, 2003: 350-370. |
| [15] | 阿茹罕. 陕西农村居民收入变化对消费结构影响研究[D]. 西安: 西安石油大学, 2015. |
| [15] | A R H. Study on the inflence of income of rural residents in Shaanxi on consumption structure [D]. Xi'an: Xi'an Shiyou University, 2015. |
/
| 〈 |
|
〉 |
