扭曲测量误差数据下部分线性空间自回归模型的估计  

Estimation of partial linear spatial autoregressive model with distorted measurement error data

作　　者：刘凤 赵培信[1,2] LIU Feng;ZHAO Peixin(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Statistical Intelligent Computingand Monitoring,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学统计智能计算与监测重庆市重点实验室,重庆400067

出　　处：《齐鲁工业大学学报》2025年第1期62-69,共8页Journal of Qilu University of Technology

基　　金：国家社会科学基金一般项目(18BTJ035);重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0006)。

摘　　要：对空气、地表水、声环境等领域的环境数据统计建模过程中常常遇到空间相关数据及扭曲测量误差数据,为解决实际统计建模中数据的空间相关性和扭曲测量误差的问题,研究了带有扭曲测量误差的部分线性空间自回归模型的估计理论。通过条件绝对均值校准方法,消除了扭曲测量误差造成的影响,该方法避免了对变量施加非零期望条件。利用校准后的变量,结合B样条逼近技术、正交投影方法和两阶段最小二乘方法,解决了模型中的内生性问题,所提出的方法消除了非参数部分对参数部分的变量选择影响,保证了所提出估计量的有效性和相合性。在一定条件下,证明了线性部分的参数估计向量的渐近正态性和非参数函数的最优收敛速度。所得结果将进一步完善空间数据统计模型的理论体系,有助于更准确地理解实际问题的数据模式和关系,为从事环境科学、生物医学以及社会科学等领域的空间数据建模提供了一种新的参考方法。Spatial correlation data and distorted measurement error data are often encountered in the process of statistical modeling of environmental data in the fields of air,surface water and acoustic environment.In order to solve the problems of spatial correlation and distorted measurement error of data in actual statistical modeling,the estimation theory of partial linear spatial autoregressive model with distorted measurement error is studied.The influence of distorted measurement error is eliminated by conditional absolute mean calibration,which avoids the imposition of non-zero expectation conditions on variables.By using the calibrated variables and combining B-spline approximation technique,orthogonal projection method and two-stage least squares method,the endogeneity problem in the model is solved.The proposed method eliminates the influence of the non-parametric part on the variable selection of the parametric part,and ensures the effectiveness and consistency of the proposed estimators.Under certain conditions,the asymptotic normality of the parameter estimation vector of the linear part and the optimal convergence rate of the non-parametric function are proved.The results obtained will further improve the theoretical system of spatial data statistical model,contribute to a more accurate understanding of data patterns and relationships in practical problems,and provide a new reference method for spatial data modeling in environmental science,biomedicine,social science and other fields.

关 键 词：扭曲测量误差 部分线性空间自回归模型 正交投影 两阶段最小二乘方法 

分 类 号：O212.7[理学—概率论与数理统计]