部分函数型线性空间自回归模型的假设检验  

Hypothesis Testing in Partial Functional Linear Spatial Autoregressive Model

作　　者：刘高生 柏杨[2] 余平[3] Gao Sheng LIU;Yang BAI;Ping YU(Tianjin University of Commerce,Tianjin 300134,P.R.China;School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,P.R.China;School of Mathematics and Computer Science,Shanxi Normal University,Taiyuan 030032,P.R.China)

机构地区：[1]天津商业大学理学院,天津300134 [2]上海财经大学统计与管理学院,上海200433 [3]山西师范大学数学与计算机学院,太原030032

出　　处：《数学学报（中文版）》2023年第2期239-252,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11771268,12071267);天津市教委科研计划资助项目(2021SK140)。

摘　　要：本文提出了部分函数型线性空间自回归模型的空间效应以及参数效应的假设检验问题.首先利用函数型主成分分析方法估计斜率函数,利用广义矩估计方法估计参数.然后利用得到的相合估计,在原假设和备择假设下,构造了基于残差平方和的检验统计量,同时给出了此检验统计量的渐近性质.模拟结果表明在有限样本下,检验统计量具有良好表现.最后将部分函数型线性空间自回归模型的检验应用到一个关于经济增长的数据案例中,说明所提出的检验统计量的应用表现.The paper proposes a hypothesis testing of spatial autoregressive and parametric component in partial functional linear spatial autoregressive model.The functional principle component analysis is employed to approximate the slope function.And generalized method of moments(GMM)is used to estimate parameters.Basis on consistent estimators,we construct a test statistic of the residual sums of squares under null and alternative hypothesis.In addition,we establish the asymptotic properties of the proposed test.Simulation studies show the proposed test has good size and power with finite sample size.Finally,a real data analysis of growth data is conducted to investigate the significance of spatial autoregressive and parametric coefficients with partial functional linear spatial autoregressive model.

关 键 词：部分函数型线性空间自回归模型 函数型主成分分析 广义矩估计 假设检验 

分 类 号：O212.1[理学—概率论与数理统计]