约束条件下线性可加空间自回归模型方法研究  

Research on Linear Additive Spatial Autoregressive Model Method Under Constraints

作　　者：刘苏兵 LIU Subing(School of Mathematics-Physics and Finance,Anhui University of Technology,Wuhu 241000,Anhui,China;Public Basic Teaching Department,Anhui Mechanical and Electrical Vocational Technical College,Wuhu 241002,Anhui,China)

机构地区：[1]安徽工程大学数理与金融学院,安徽芜湖241000 [2]安徽机电职业技术学院公共基础教学部,安徽芜湖241002

出　　处：《西昌学院学报（自然科学版）》2024年第3期69-77,共9页Journal of Xichang University(Natural Science Edition)

摘　　要：[目的]针对空间依赖性问题,提出约束条件下线性可加空间自回归模型的统计推断方法。[方法]先对线性可加空间自回归模型增加线性约束条件。通过B样条基函数近似求解未知的平滑函数,并代入回归模型,生成包含B样条基函数的空间自回归模型,对此模型的损失函数进行最小化,获取约束条件下模型的稀疏估计,通过SCAD惩罚函数无偏估计较大系数。在10种约束条件下,研究了线性可加空间自回归模型估计的渐近性质,得到在最优收敛速度下进行斜率系数的估计时,函数项部分不会改变参数估计的渐近分布特性。[结果]实验结果表明,该方法不仅在理论上具有可行性,而且在实践中易于操作。相比非约束估计,约束稀疏估计更为优秀。[结论]在交通数据统计分析中,该方法具有实用性和有效性。[Objective]To propose a statistical inference method for linear additive spatial autoregressive models under constraint conditions to address spatial dependency issues.[Method]First,linear constraints are added to the linear ad‐ditive spatial autoregressive model.By approximating the unknown smoothing function using B-spline basis functions and substituting it into the regression model,a spatial autoregressive model containing B-spline basis functions is generated.The loss function of this model is minimized to obtain a sparse estimate of the model under constraint conditions.The SCAD penalty function is used to estimate the larger coefficients without bias.The asymptotic properties of linear additive space autoregressive model estimation were studied under 10 constraint conditions,and it was found that when estimating the slope coefficient at the optimal convergence speed,the asymptotic distribution characteristics of the parameter esti‐mation were not affected by the function term.[Result]The experimental results show that this method is not only feasible in theory,but also easy to operate in practice.Compared to unconstrained estimation,constrained sparse estimation is superior.[Conclusion]This method is practical and effective in traffic data statistical analysis.

关 键 词：约束条件 线性可加 空间自回归模型 统计推断方法 稀疏估计 渐近性质 

分 类 号：O212.1[理学—概率论与数理统计]