Abstract

Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance is introduced. Furthermore, we propose the jackknife estimator, jackknife and adjust jackknife empirical log-likelihood ratios of the error variance and establish their asymptotic distributions. Simulation studies in terms of coverage probability and average length of confidence intervals are conducted to evaluate the proposed method. A real data set is used to illustrate the proposed JEL and AJEL methods.

摘要

在实践中经常会出现测量错误和缺失数据。在这种情况下，我们专注于使用折刀经验似然（JEL）和调整折刀经验似然（AJEL）方法来构建线性模型中误差方差的置信区间。基于模型的残差，引入了误差方差的偏差校正逆概率加权估计量。此外，我们提出了折刀估计器、折刀和调整折刀误差方差的经验对数似然比，并建立了它们的渐近分布。对覆盖概率和置信区间的平均长度进行了仿真研究，以评估所提出的方法。一个真实的数据集用于说明所提出的 JEL 和 AJEL 方法。