Empirical likelihood (EL) has been extensively studied to make statistical inferences for independent and dependent observations. However, it experiences the problem of under‐coverage which causes the coverage probability of the EL‐based confidence intervals to be lower than the nominal level, especially in small sample sizes. In this paper, we propose modified versions of different EL‐related methods to tackle this issue, including the adjusted EL, the EL with theoretical Bartlett correction and the EL with estimated Bartlett correction for short‐memory time series models. Asymptotic distributions of the likelihood‐type statistics are established as the standard chi‐square distribution. Simulations are conducted to compare coverage probabilities with other existing methods under different distributions. Two real data set applications demonstrate how to construct confidence regions of parameters.

中文翻译：

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基于修正的经验似然的短时间序列模型推断

对经验似然（EL）进行了广泛研究，以对独立和从属观察进行统计推断。但是，它会遇到覆盖不足的问题，这会导致基于EL的置信区间的覆盖概率低于名义水平，尤其是在小样本量中。在本文中，我们针对不同的EL相关方法提出了修改版本，以解决此问题，包括调整后的EL，具有理论Bartlett校正的EL和具有估计的Bartlett校正的EL用于短时间时间序列模型。建立似然类型统计量的渐近分布作为标准卡方分布。进行模拟以比较覆盖率与其他现有方法在不同分布下的覆盖率。