半参数顺序回归的贝叶斯推断

doi:10.12066/j.issn.1007-2861.2124

上海大学学报(自然科学版) ›› 2021, Vol. 27 ›› Issue (1): 218-226.doi: 10.12066/j.issn.1007-2861.2124

• 研究论文 • 上一篇

半参数顺序回归的贝叶斯推断

赵焕丽, 何幼桦()

上海大学理学院, 上海 200444

收稿日期:2019-03-06 出版日期:2021-02-28 发布日期:2021-02-28
通讯作者: 何幼桦 E-mail:heyouhua@t.shu.edu.cn
作者简介:何幼桦(1960---), 男, 副教授, 博士, 研究方向为整理统计. E-mail: heyouhua@t.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11471208)

Bayesian inference for semiparametric ordinal regression

ZHAO Huanli, HE Youhua()

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2019-03-06 Online:2021-02-28 Published:2021-02-28
Contact: HE Youhua E-mail:heyouhua@t.shu.edu.cn

摘要/Abstract

摘要：

结合比例优势模型和半参数回归模型建立了一般形式的半参数顺序回归模型. 对于模型的参数与非参数部分, 构造了基于随机过程有限维分布的贝叶斯估计量, 并在正态情形下给出了估计量的解析表达式. 数值模拟结果表明, 即使在小样本情况下, 模型参数的估计值也接近真实值, 非参数部分的估计值能描绘出真实函数的形状. 对根据家庭消费结构预测收入等级的实证分析表明, 相同收入等级的城镇居民与农村居民家庭的消费结构存在差异, 外推情形下也有较理想的表现.

关键词: 半参数回归, 顺序变量, 贝叶斯估计, 有限维分布, 收入等级预测

Abstract:

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.

Key words: semiparametric regression, ordinal variables, Bayesian estimation, finite dimensional distribution, income level prediction

中图分类号:

O212.8

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.

ZHAO Huanli, HE Youhua. Bayesian inference for semiparametric ordinal regression[J]. Journal of Shanghai University（Natural Science Edition）, 2021, 27(1): 218-226.

图/表 3

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半参数顺序回归的贝叶斯推断

Bayesian inference for semiparametric ordinal regression

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