含空间自相关误差项的非参数回归模型的调整经验似然估计  

Adjusted empirical likelihood for nonparametric regression model with spatial autoregressive error

作　　者：邹云龙 Zou Yunlong(Department of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《湖南文理学院学报（自然科学版）》2023年第3期20-25,31,共7页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：广西研究生教育创新计划项目(YJSCXP202104)。

摘　　要：利用调整经验似然的方法,研究了含空间自相关误差项的非参数回归模型的调整经验似然估计问题。通过鞅差序列处理该模型估计方程中出现的线性二次型形式,构造出该模型的经验似然比统计量。针对经验似然估计方程可能不存在解的情况构造调整经验似然比统计量,证明了该调整经验似然比统计量是渐近卡方分布的,并且对该调整经验似然比统计量的渐进功效进行了研究。This paper investigates the problem of adjusting the empirical likelihood estimation of a nonparametric regression model with a spatially autocorrelated error term by using the adjusted empirical likelihood method.The empirical likelihood ratio statistic of the model is constructed by processing the linear-quadratic forms in the estimating equation of the model through the martingale difference sequence.The adjusted empirical likelihood ratio statistic is constructed for the case that the empirical likelihood estimating equations may not have a solution.In this paper,we prove that the adjusted empirical likelihood ratio statistics are chi-squared distributions,and investigate the asymptotic efficacy of the adjusted empirical likelihood ratio statistics.

关 键 词：非参数回归函数 调整经验似然 鞅差序列 

分 类 号：O212.7[理学—概率论与数理统计]