固定效应部分线性单指数面板模型的快速有效估计及应用  

Fast efficient estimation and application of partially linear single index model with fixed effects

作　　者：丁飞鹏[1] 陈建宝 DING Fei-peng;CHEN Jian-bao(School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China;College of Mathematics and Informatics,Fujian Normal University,Fuzhou 350117,China;Fujian Provincial Engineering Technology Research Center for Public Service,Fuzhou 350117,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022 [2]福建师范大学数学与信息学院,福建福州350117 [3]福建省公共服务大数据挖掘与应用工程技术工程中心,福建福州350117

出　　处：《高校应用数学学报（A辑）》2019年第2期127-141,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家社会科学基金(16BTJ018);教育部人文社会科学重点研究基地重大项目(15JJD790029);福建省自然科学基金(2017J01396; 2018J05002);福建省高等学校科技创新团队项目(IRTSTFJ);福建师范大学创新团队项目(IRTL1704)

摘　　要：将最小二乘支持向量机(LSSVM)和二次推断函数法(QIF)相结合,构造了个体内具有相关结构的固定效应部分线性单指数面板模型的新估计方法;在一定的正则条件下,证明了参数估计量的渐近正态性,导出了非参数估计量的收敛速度;Monte Carlo模拟了所述方法在各种相关结构下的有限样本表现,并与惩罚二次推断函数(PQIF)法进行了比较;将估计技术应用于分析我国人口结构与居民消费率的关系.研究发现,该方法改善了估计量的有效性,应用效果良好,程序运行速度快,适合经济变量间的线性和非线性关系研究以及大数据分析.By combination of least square vector machine(LSSVM) with quadratic inference functions(QIF),this paper construct a new estimation method for partially linear single index panel model with fixed effects when responses from the same cluster are correlated. Under some regular condition,asymptotic normality of parametric estimators and convergence rate of non-parametric estimator are derived. The finite sample performances of the proposed method are investigated by Monte Carlo simulation under different correlation structures, and compared with penalized quadratic inference functions method(PQIF). The proposed estimation techniques are applied to analyse the relationship between population structure and residents’ consumption rate. Our research results show that the efficiency of estimators are improved by the proposed method, application effects are good, program operation has high speed, it is particularly suitable for analysis of linear, nonlinear relationship among economic variables and big data.

关 键 词：固定效应部分线性单指数面板模型 最小二乘支持向量机 二次推导函数法 渐近性 MONTE CARLO模拟 

分 类 号：O212.1[理学—概率论与数理统计]