测量误差数据下偏正态众数回归模型的参数估计  

Parameter Estimation for Skew-normal Mode Regression Model with Measurement Error

作　　者：阳杰 曾鑫 吴刘仓[1] YANG JIE;ZENG XIN;WU LIUCANG(Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China)

机构地区：[1]昆明理工大学理学院,昆明650500

出　　处：《应用数学学报》2023年第4期606-621,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12261051);昆明理工大学学生课外学术科技创新基金(批准号:2022KJ151)资助项目。

摘　　要：现有对回归模型的研究大多仅限于直接观测的解释变量,忽略数据的测量误差将增加模型参数的估计偏差.目前关于测量误差模型的研究主要集中在回归误差服从正态分布的假设,这种假设不适用于研究非对称的数据。对于偏斜数据,众数的代表性优于均值和中位数.本文基于测量误差数据介绍了偏正态众数回归模型,并通过EM算法估计了模型的参数.模拟研究的结果表明,协变量带测量误差下的众数回归比均值回归有更好的表现.通过实例分析进一步表明了所提出模型和方法的有效性。Existing research on regression models are limited to directly observed ex-planatory variables,which increases the error of estimation.The existing studies on models with measurement error mainly focus on the normality assumption of regression error.However,it is not reasonable to use the assumption to study asymmetric data.The performance of the mode is better than that of the mean and median for skewed data.Considering measurement error data,this paper will introducethe skew-normal mode regression model,and extend an EM algorithm which is developed to estimate the parameters based on the traditional method.The results of simulation study in-dicate that the performance of mode regression is better than mean regression when covariates with measurement error.A real example is further provided to investigate the performance of the proposed methodologies.Emulation experiments and instance analysis show that the model and the proposed parameter estimation method have strong practicability and effectiveness.

关 键 词：测量误差数据 众数回归模型 偏正态分布 EM算法 

分 类 号：O212.8[理学—概率论与数理统计]