部分函数线性模型的调整经验似然估计
Adjusted Empirical Likelihood Estimation for Partial Functional Linear Models
DOI: 10.12677/sa.2025.147197, PDF,    科研立项经费支持
作者: 蒙海苗*, 吕 蒙：广西科技师范学院数学与计算机工程学院，广西 来宾；贾慧英：桂林师范学院教育系，广西 桂林
关键词: 部分函数线性模型；调整经验似然；置信域；Partial Functional Linear Model； Adjusted Empirical Likelihood； Confidence Region
摘要: 本文主要利用调整经验似然的理论，研究部分函数线性回归模型中感兴趣参数的估计问题。通过构造回归系数的调整对数经验似然比统计量，并从理论上给出该估计量的统计性质，即在满足一定的条件下，这个统计量是渐近服从于卡方分布的，接着给出渐近性质的理论证明。最后，利用这一理论性质构造回归系数的置信域。
Abstract: This paper mainly studies the problem of adjusted empirical likelihood estimation of partial function linear regression models, constructs the adjusted empirical likelihood ratio statistic of regression coefficients, and further gives the statistical properties of the estimator in theory, that is, under certain conditions, the statistic is asymptotically subject to chi square distribution, and gives theoretical proof, using this result to construct the confidence region of regression coefficients.
文章引用：蒙海苗, 贾慧英, 吕蒙. 部分函数线性模型的调整经验似然估计[J]. 统计学与应用, 2025, 14(7): 202-209. https://doi.org/10.12677/sa.2025.147197

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