函数型部分线性单指标空间自回归模型  

Functional partial linear single index spatial autoregressive model

作　　者：李云霞 王心愉 LI Yun-xia;WANG Xin-yu(School of Data Sciences,Zhejiang University of Finance and Economics,Hangzhou 310018,China;School of Data Science and Arti¯cial Intelligence,Wenzhou University of Technology,Wenzhou 325035,China)

机构地区：[1]浙江财经大学数据科学学院,浙江杭州310018 [2]温州理工学院数据科学与人工智能学院,浙江温州325035

出　　处：《高校应用数学学报（A辑）》2023年第2期151-165,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：教育部人文社会科学研究规划基金(22YJA910001)。

摘　　要：该文提出了函数型部分线性单指标空间自回归模型,该模型综合并拓展了函数型单指标模型和空间自回归模型.基于拟极大似然估计(QMLE)和局部线性方法,构造了一个四阶段估计器来估计参数和非参数分量,并由假设条件给出了参数和非参数分量估计的渐近性质.在此基础上,通过Monte Carlo模拟研究了估计器的有限样本性能,最后对加拿大气象数据的年总降雨量和日均气温曲线建立了函数型单指标空间自回归模型,研究发现年总降雨量存在负向空间自相关性,日均气温与年总降雨量正相关.This paper presents a functional partial linear single index spatial autoregressive model,which synthesizes and extends the functional single index model and spatial autoregressive model(SAR).Based on the quasi maximum likelihood estimation(QMLE)and local linear method,a four stage esti-mator is constructed to estimate parametric and nonparametric components.The asymptotic properties of parametric and nonparametric component estimators are given build on the assumptions.On this basis,the limited sample performance of the estimator is studied by Monte Carlo simulation.Finally,a functional data spatial single index autoregressive model is established for the curves of annual total rainfall and daily average temperature of Canadian meteorological data.It is found that there is a weak negative spatial autocorrelation for the total rainfall in this model,and the daily average temperature is positively correlated with the annual total rainfall.

关 键 词：空间自回归模型 函数型数据 单指标模型 QMLE 局部线性回归 

分 类 号：O212.7[理学—概率论与数理统计]