半参数函数型线性空间自回归模型的统计推断及应用  

Statistical inference and application of semi-parametric functional linear spatial autoregressive model

作　　者：惠姣姣 HUI Jiaojiao(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji Shaanxi 721013)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《首都师范大学学报（自然科学版）》2023年第6期20-29,共10页Journal of Capital Normal University：Natural Science Edition

基　　金：陕西省教育厅自然科学研究项目(202310592)。

摘　　要：为了解决自变量为函数型数据、响应变量为标量数据、协变量为矩阵型数据且其分布未知的问题,本文提出半参数函数型线性空间自回归模型(SP-FLSARM)。首先利用函数型主成分分析(FPCA)处理函数型自变量,利用B样条估计非参数连接函数;其次利用极大似然估计(MLE)得到未知参数的估计值;最后针对西班牙气象台的温度数据建立SP-FLSARM模型。相较于函数型线性空间自回归模型(FLSARM)和函数型线性模型(FLM),SP-FLSARM的方差和残差方差比(VR)最小,即SP-FLSARM的模型拟合效果最好。In order to solve the problem that the independent variable is functional data,the response variable is scalar data,the covariant is matrix data and its distribution is unknown,this paper proposes a semi-parametric functional linear spatial autoregressive model(SP-FLSARM).Firstly,the functional independent variable is processed by functional principal component analysis(FPCA),the non-parametric connection function is estimated by B-spline.Secondly,the estimated value of the unknown parameter is obtained by maximum likelihood estimation(MLE).Finally,the SP-FLSARM model is established based on the temperature data of the Spanish meteorological observatory.Compared with functional linear spatial autoregressive model(FLSARM)and functional linear model(FLM),the variance and variance ratio(VR)of SP-FLSARM are the smallest,the fitting effect of SP-FLSARM is the best.

关 键 词：SP-FLSARM FPCA B样条 MLE 西班牙气象台温度数据 

分 类 号：O212.1[理学—概率论与数理统计]