空间自相关性异质特征的局部极大似然估计及在手足口病防护中的应用  

Local Maximum Likelihood Estimation of Heterogeneous Features with Spatial Autocorrelation and Its Application in Protection of Hand-Foot-Mouth Disease

作　　者：杨晓兰 张辉国[1] 胡锡健[1] YANG Xiaolan;ZHANG Huiguo;HU Xijian(School of Mathematics and Systems Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《广西师范大学学报(自然科学版)》2025年第2期179-192,共14页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11961065);新疆自然科学基金(2023D01C01);教育部人文社会科学研究规划基金(19YJA910007)。

摘　　要：空间自回归模型广泛用于空间数据的相关性分析,它将空间自回归系数设定为全局常数,对空间自相关性的同质特征进行建模,但是无法分析研究区域内局部异质的空间自相关特征。本文研究一类异质性空间自回归变系数模型,将模型中的空间自相关回归系数设为随地理位置发生变化的变系数函数,实现同时对空间自相关性的局部异质特征和非平稳回归关系建模,提出异质性空间自回归变系数模型的局部常数极大似然和局部线性极大似然估计方法。进行数值模拟,结果表明:局部线性极大似然估计和局部常数极大似然估计方法在有限样本下具有一致性和有效性,本文所提出的模型和估计方法具有良好表现。利用所研究的模型和提出的估计方法对2018年我国手足口病发病率与影响因素进行分析,发现各省(自治区、直辖市)的局部空间自相关性呈现西部偏高,中部和东部偏低的趋势,存在一定差异性,各影响因素对手足口病发病率的影响程度也随空间位置的变化而有所不同。Spatial autoregressive models are widely used for correlation analysis of spatial data,setting the spatial autoregression coefficient as a global constant to model the homogeneous features of spatial autocorrelation,but cannot be used to analyze the locally heterogeneous spatial autocorrelation features within the study area.In this paper,a class of heterogeneous spatial autoregressive varying coefficient models is studied,and the local constant maximum likelihood and local linear maximum likelihood estimation methods of the heterogeneous spatial autoregressive varying coefficient models are proposed by setting the spatial autocorrelation regression coefficient in the models as varying coefficient function that changes with geographical location to realize the modeling of local heterogeneous features and nonstationary regression relations of spatial autocorrelation at the same time.Through numerical simulation,the results show that the local linear maximum likelihood estimation and local constant maximum likelihood estimation methods have consistency and effectiveness under finite samples,and the model and estimation method proposed in this paper have good performance.The proposed models and methods are used to analyze hand-foot-mouth disease(HFMD)incidence and influencing factors based on data within the territory of China in 2018.It is found that the local spatial autocorrelation of each province shows a trend of being higher in the west and lower in the central eastern regions.The extent of the impact of each influencing factor on the incidence of HFMD also varies with spatial location.

关 键 词：异质性空间自回归变系数模型 空间自相关异质性 局部常数极大似然 局部线性极大似然 手足口病 

分 类 号：O212.1[理学—概率论与数理统计]