• 论文 •

### 变系数线性EV模型参数的调整加权最小二乘估计及其渐近性质

1. 北京师范大学数学科学学院, 统计数据分析实验室, 北京 100875
• 收稿日期:2006-09-30 修回日期:1900-01-01 出版日期:2007-02-25 发布日期:2007-02-25

Cui Hengjian. ADJUST WEIGHTED LS ESTIMATION FOR THE PARAMETER IN THE VARYING COEFFICIENTS LINEAR EV MODEL[J]. Journal of Systems Science and Mathematical Sciences, 2007, 27(1): 82-92.

### ADJUST WEIGHTED LS ESTIMATION FOR THE PARAMETER IN THE VARYING COEFFICIENTS LINEAR EV MODEL

Cui Hengjian

1. School of Mathematical Sciences, Statistical Data Analysis Laboratory, Beijing Normal University, Beijing 100875
• Received:2006-09-30 Revised:1900-01-01 Online:2007-02-25 Published:2007-02-25

It is well known that the regression coefficients are considered to be constant in the liner errors-in-variables (EV) model. In many applications, however, the coefficients may be varying with a covariate, such as time, temperature and so on. This paper gives such examples, and introduces how to estimate the coefficients when the coefficients are varying with a covariate in the structural linear EV model. Under the identification of cov-variance matrix of measurements error is known, we propose the adjust weighted LS estimators (AWLSE) for the estimated parameters of varying regression coefficients as well as the variance of model error. It is shown that the AWLSEs are strongly consistent and asymptotically normal under some mild conditions. Simulations illustrate our AWLSEs have good performance.

MR(2010)主题分类:

()
 [1] 王江峰, 李国定, 郦颖蕾, 熊怡. 删失指标随机缺失下条件分位数的加权双核局部线性估计[J]. 系统科学与数学, 2021, 41(9): 2621-2642. [2] 范国良, 饶诗文, 王江峰. 缺失数据下变系数部分非线性测量误差模型的经验似然估计[J]. 系统科学与数学, 2021, 41(9): 2643-2659. [3] 丁飞鹏. 部分线性变系数空间自回归面板模型的有效估计及应用[J]. 系统科学与数学, 2021, 41(9): 2660-2677. [4] 刘艳霞, 王芝皓, 芮荣祥, 田茂再. 广义函数型部分变系数混合模型的估计[J]. 系统科学与数学, 2021, 41(6): 1742-1760. [5] 胡雪梅, 韦小凡. 半变系数模型研究美国爱荷华州埃姆斯市的房价问题[J]. 系统科学与数学, 2021, 41(1): 269-279. [6] 牛娟，谢田发，郭媛媛，孙志华. 协变量有测量误差时Tobit回归模型的估计[J]. 系统科学与数学, 2020, 40(9): 1672-1686. [7] 李晨露.  大数据下广义线性模型的参数估计算法[J]. 系统科学与数学, 2020, 40(5): 927-940. [8] 王彦. 固定设计下计算机模型$L_2$校准的渐近性质[J]. 系统科学与数学, 2020, 40(2): 252-261. [9] 贾锴. DRE年龄性质的非参数检验[J]. 系统科学与数学, 2019, 39(6): 977-989. [10] 王江峰，范国良，温利民. 删失指标随机缺失下回归函数的复合分位数回归估计[J]. 系统科学与数学, 2018, 38(11): 1347-1362. [11] 周小双，张明峰，赵培信. 纵向数据下变系数部分非线性模型的经验似然推断[J]. 系统科学与数学, 2017, 37(3): 885-898. [12] 金君，戴家佳，杜彦斌. 单指标变系数模型的B样条估计[J]. 系统科学与数学, 2017, 37(12): 2427-2442. [13] 邹清明，朱仲义. 部分线性单指标模型的M-估计[J]. 系统科学与数学, 2016, 36(11): 2099-2117. [14] 李静，柴树根. 一类具有半线性多孔声学边界条件的变系数波方程的能量衰减性[J]. 系统科学与数学, 2016, 36(1): 37-52. [15] 郭文雯,崔恒建.  带自回归过程的单指标模型的参数估计及其渐近性质[J]. 系统科学与数学, 2015, 35(12): 1463-1478.