基于广义Hukuhara差的区间数回归模型及参数估计  

Interval-Value Regression Model and Parameter Estimation Based on Generalized Hukuhara Difference

作　　者：王启明[1] 王清涵 周亮[1] WANG Qiming;WANG Qinghan;ZHOU Liang(School of Mathematics,Hohai University,Nanjing 210098)

机构地区：[1]河海大学数学学院,南京210098

出　　处：《系统科学与数学》2025年第2期630-638,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家重点研发计划(2022YFB3207400);江苏省研究生科研与实践创新计划(422003263)资助课题。

摘　　要：区间值数据比点值数据包含更多的信息,已成为复杂大数据背景下应用研究的热点.现有的区间数回归模型大多基于代表元素框架或者传统区间数减法构建,但代表元素框架模型未把区间整体参加运算易丢失区间信息,传统区间数减法存在区间数运算结果不合理现象.为解决上述问题,文章提出区间数广义Hukuhara(gH)差的框架下p维区间数线性回归模型,在保证区间运算结果合理的基础上,基于支撑函数构建回归残差评估方法,推导了模型的最小二乘估计,并讨论了一维情况下回归参数的形态、特点、性质.最后利用蒙特卡罗模拟验证了新方法的有效性和精度.Interval-value data contains more information than point-value data,which has become a hot topic in the application of complex big data.Most of the existing interval-value regression models are built on the basis of representative element framework or traditional interval-value subtraction,but the representative element framework model does not involve the whole interval in the operation,and the traditional interval-value subtraction has unreasonable operation results.In order to solve the above problems,this paper proposes a-dimensional interval-value regression model under the framework of generalized Hukuhara(gH)difference.On the basis of ensuring reasonable interval operation results,a regression residual evaluation method is constructed based on the support function.The least squares estimation is derived,and the characteristics of the regression parameters under 1-dimensional condition are discussed.Finally,Monte Carlo simulation is used to verify the effectiveness and accuracy of the new method.

关 键 词：广义Hukuhara差 区间数线性回归 参数估计 蒙特卡罗模拟 

分 类 号：O212.1[理学—概率论与数理统计]