线性模型的经验无偏刀切Liu估计
Empirical Unbiased Jackknifed Liu Estimator in Linear Model
DOI: 10.12677/aam.2025.146305, PDF,    国家自然科学基金支持
作者: 程锦鸽：东华理工大学理学院，江西 南昌；彭 萍*：东华理工大学经济与管理学院，江西 南昌
关键词: 经验无偏估计；刀切Liu估计；线性模型；均方误差均阵；Empirical Unbiased Estimator； Jackknifed Liu Estimator； Linear Model； Mean Square Error Matrix
摘要: 本文主要对线性模型中回归系数的经验无偏刀切Liu估计进行研究。首先，在刀切Liu估计的基础上构造了经验无偏刀切Liu估计；其次，基于均方误差准则分析了该估计的优良性质。最后，基于数值模拟和实例分析论证了估计的优良性质。结果表明：提出的经验无偏刀切Liu估计在具有无偏性的同时一致优于普通最小二乘估计，并在一定的条件下优于Liu估计和刀切Liu估计。
Abstract: In this paper, we mainly investigate the empirical unbiased Jackknifed Liu estimator of regression coefficient in linear model. Firstly, an unbiased Jackknifed Liu estimator with prior information is obtained based on the Jackknifed Liu estimator. Secondly, the excellent properties of the estimator are analyzed based on mean square error matrix. Finally, numerical simulation and real data analysis are used to demonstrate the dominance property. It is shown that empirical unbiased Jackknifed Liu estimator is consistently superior to ordinary least square estimator while maintaining unbiasedness, and outperforms both Liu estimator and Jackknifed Liu estimator.
文章引用：程锦鸽, 彭萍. 线性模型的经验无偏刀切Liu估计[J]. 应用数学进展, 2025, 14(6): 104-118. https://doi.org/10.12677/aam.2025.146305

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