We use the jackknife to bias correct the log-periodogram regression (LPR) estimator of the fractional parameter in a stationary fractionally integrated model. The weights for the jackknife estimator are chosen in such a way that bias reduction is achieved without the usual increase in asymptotic variance, with the estimator viewed as `optimal' in this sense. The theoretical results are valid under both the non-overlapping and moving-block sub-sampling schemes that can be used in the jackknife technique, and do not require the assumption of Gaussianity for the data generating process. A Monte Carlo study explores the A–nite sample performance of di§erent versions of the optimal jackknife estimator under a variety of fractional data generating processes. The simulations reveal that when the weights are constructed using the true parameter values, a version of the optimal jackknife estimator almost always out-performs alternative bias-corrected estimators. A feasible version of the jackknife estimator, in which the weights are constructed using consistent estimators of the unknown parameters, whilst not dominant overall, is still the least biased estimator in some cases.

中文翻译：

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分数参数的对数周期图估计器的最佳偏差校正：折刀法

我们使用 jackknife 对平稳分数积分模型中分数参数的对数周期图回归 (LPR) 估计量进行偏置校正。jackknife 估计器的权重以这样一种方式选择，即在不增加渐近方差的情况下实现偏差减少，在这个意义上，估计器被视为“最佳”。理论结果在可用于折刀技术的非重叠和移动块子采样方案下都是有效的，并且不需要对数据生成过程进行高斯假设。Monte Carlo 研究探索了不同版本的最佳折刀估计器在各种部分数据生成过程下的无限样本性能。模拟表明，当使用真实参数值构建权重时，最佳折刀估计器的一个版本几乎总是优于替代偏差校正估计器。jackknife 估计器的一个可行版本，其中权重是使用未知参数的一致估计器构建的，虽然总体上不占主导地位，但在某些情况下仍然是最小偏差的估计器。