Bartlett Correction of Empirical Likelihood for Non‐Gaussian Short‐Memory Time Series
证明了对于短记忆时间序列，即使创新项非高斯，经验似然的Bartlett校正仍可将置信区域的覆盖误差从O(n^{-1})降至O(n^{-2})，适用于单参数模型且已知创新方差和零均值的情形。
Bartlett correction, which improves the coverage accuracies of confidence regions, is one of the desirable features of empirical likelihood. For empirical likelihood with dependent data, previous studies on the Bartlett correction are mainly concerned with Gaussian processes. By establishing the validity of Edgeworth expansion for the signed root empirical log‐likelihood ratio statistics, we show that the Bartlett correction is applicable to empirical likelihood for short‐memory time series with possibly non‐Gaussian innovations. The Bartlett correction is established under the assumptions that the variance of the innovation is known and the mean of the underlying process is zero for a single parameter model. In particular, the order of the coverage errors of Bartlett‐corrected confidence regions can be reduced from O ( n −1 ) to O ( n −2 ).