半参数顺序变量回归模型

doi:10.3969/j.issn.1007-2861.2014.04.010

上海大学学报(自然科学版) ›› 2016, Vol. 22 ›› Issue (4): 477-485.doi: 10.3969/j.issn.1007-2861.2014.04.010

半参数顺序变量回归模型

熊笛, 何幼桦

上海大学理学院, 上海200444

收稿日期:2014-11-21 出版日期:2016-08-30 发布日期:2016-08-30
通讯作者: 何幼桦(1960—), 男, 教授, 博士, 研究方向为概率统计. E-mail: heyouhua@shu.edu.cn
作者简介:何幼桦(1960—), 男, 教授, 博士, 研究方向为概率统计. E-mail: heyouhua@shu.edu.cn
基金资助:
国家自然科学基金资助项目(11371242)

Semi-parametric ordinal variable regression model

XIONG Di, HE Youhua

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2014-11-21 Online:2016-08-30 Published:2016-08-30

摘要/Abstract

摘要：

在比例优势模型基础上对顺序变量回归模型作更一般的推广, 建立了半参数顺序变量回归模型, 构造了模型中的线性和非线性部分的估计量, 并证明了该估计量的弱相合性. 通过数值模拟, 考察了不同样本容量下半参数顺序变量回归的判断正确率和回归函数的均方误差.实验结果表明: 半参数顺序回归模型在小样本情况下仍具有较高精度, 并且在实验点处的重复次数相对于观察点个数对精度影响更大. 通过对粮食预警实例的计算表明, 半参数顺序回归模型较比例优势线性模型具有更好的外推效果.

关键词: 顺序变量回归 , 半参数回归, 比例优势模型

Abstract:

Based on a proportional odds model, the ordinal variable regression model is generalized, a semi-parametric ordinal regression model is established, and consistency of the estimators both in linear and nonlinear parts are proved in this paper. Simulation is conducted to analyze the correct rate and mean square error in the semi-parametric ordinal variable regression model with different sample sizes. The result shows that the semi-parametric ordinal regression model has high accuracy even with small samples. Compared to the number of observation points, the repeat number of experimental points has greater influence on accuracy. Calculation of the grain price warning problem shows that the semi-parametric ordinal regression model provides better extrapolation results than the proportional odds model.

Key words: ordinal variable regression , semi-parametric regression, proportional odds model

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.

XIONG Di, HE Youhua. Semi-parametric ordinal variable regression model[J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(4): 477-485.

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半参数顺序变量回归模型

Semi-parametric ordinal variable regression model

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