Bias correction can often improve the finite sample performance of estimators. We show that the choice of bias correction method has no effect on the higher-order variance of semiparametrically efficient parametric estimators, so long as the estimate of the bias is asymptotically linear. It is also shown that bootstrap, jackknife, and analytical bias estimates are asymptotically linear for estimators with higher-order expansions of a standard form. In particular, we find that for a variety of estimators the straightforward bootstrap bias correction gives the same higher-order variance as more complicated analytical or jackknife bias corrections. In contrast, bias corrections that do not estimate the bias at the parametric rate, such as the split-sample jackknife, result in larger higher-order variances in the i.i.d. setting we focus on. For both a cross-sectional MLE and a panel model with individual fixed effects, we show that the split-sample jackknife has a higher-order variance term that is twice as large as that of the `leave-one-out' jackknife.

翻译：偏差校正通常能提升估计量的有限样本表现。研究表明，只要偏差估计量是渐近线性的，偏差校正方法的选择对半参数有效参数估计量的高阶方差没有影响。同时，对于具有标准形式高阶展开式的估计量，Bootstrap法、Jackknife法和解析偏差估计均具有渐近线性特征。特别地，我们发现对于多种估计量而言，直接使用Bootstrap偏差校正与更复杂的解析或Jackknife偏差校正具有相同的高阶方差。相比之下，未按参数速率估计偏差的校正方法（如分割样本Jackknife）会在我们关注的独立同分布设定下产生更大的高阶方差。对于截面最大似然估计和含个体固定效应的面板模型，分割样本Jackknife的高阶方差项是"留一法"Jackknife的两倍。