摘要
针对利用现有CCRM(Constrained Center-and-Range Method)方法在解决区间数回归问题中,在提高均方根误差精度的同时难以兼顾观测区间和预测区间重合度的缺陷,文章提出一种实现观测区间和预测区间具有最差重叠区的样本的重合度最大化,以及使得中点及半径误差平方和最小化的非线性回归模型;证明了该非线性回归模型是一个满足K-T条件的凸规划问题。利用蒙特卡洛模拟对所提出的优化模型进行评价,结果表明:当模型只考虑中点及半径误差平方和最小化时,优化模型退化为CCRM;模型且结果优于CCRM模型;当优化模型只考虑观测区间和预测区间具有最差重叠区的样本的重合度最大化时,该模型优于CCRM;模型。
It is difficult to give consideration to the coincidence degree of observation interval and prediction interval while improving the accuracy of root mean square error in using the existing CCRM(Constrained Center-and-Range Method) to deal with the interval regression. In view of the above defect, this paper proposes a nonlinear regression model to maximize the coincidence degree of samples with the worst coincidence between the observation interval and the prediction interval, and to minimize the sum of squares of errors of midpoints and radii, and then proves that the nonlinear regression model is a convex programming problem satisfying K-T condition. Finally, the paper employs Monte Carlo simulation to evaluate the proposed optimization model. The results show that when the model only considers the midpoints and minimizes the sum of radius error squares, the optimization model degenerates into CCRM;model, with the results superior to CCRM model, and that when the optimization model only considers the maximization of the coincidence degree of the samples with the worst coincidence between the observation interval and the prediction interval, the proposed model is superior to the CCRM;model.
作者
汪瑜
鄢仕林
何凡
Wang Yu;Yan Shilin;He Fan(School of Airport Engineering and Transportation M anagement,Civil Aviation Flight University of China,Guanghan Sichuan 618307,China)
出处
《统计与决策》
CSSCI
北大核心
2022年第5期11-16,共6页
Statistics & Decision
基金
国家自然科学基金资助项目(U1733127)
四川省科技厅社会发展领域重点研发计划(2020YFS0541)
中国民航飞行学院民航运输规划智能决策研究所计划项目(JG2019-32)
中飞院研究生创新创业项目(X2021-13)。
关键词
回归分析
区间数回归
区间数据
CCRM
中点半径法
regression analysis
interval regression
interval data
CCRM
center-and-range method