Abstract

In this paper, we apply the profile least-square method and inverse probability weighted method to define estimation of the error variance in partially linear varying-coefficient model when the covariates are missing at random. At the same time, we construct a jackknife estimator and jackknife empirical likelihood (JEL) statistic of the error variance, respectively. It is proved that the proposed estimators are asymptotical normality and the JEL statistic admits a limiting standard chi-square distribution. A simulation study is conducted to compare the JEL method with the normal approximation approach in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on sample means, biases and mean square errors under different settings. Subsequently, a real data set is analyzed for illustration of the proposed methods.

摘要

在本文中，我们应用轮廓最小二乘法和逆概率加权法来定义当协变量随机缺失时部分线性变系数模型中误差方差的估计。同时，我们分别构建了误差方差的折刀估计量和折刀经验似然 (JEL) 统计量。证明了所提出的估计量是渐近正态性的，并且 JEL 统计量承认限制标准卡方分布。进行模拟研究以在覆盖概率和平均间隔长度方面比较 JEL 方法与正态近似方法，并根据不同设置下的样本均值、偏差和均方误差对所提出的估计量进行比较。随后，