We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five applications: (i) a simple location model for i.i.d. data, possibly with infinite variance; (ii) regression models with omitted controls; (iii) inference on a target parameter based on model averaging; (iv) ridge-type regularized estimators; and (v) dynamic panel data models.

翻译：我们考虑了偏差估计值的“靴杆”推断值,我们发现,即使对偏差术语无法一致估计,通过正确执行“靴杆”可以得出有效的推断值。具体地说,我们表明,最初建议进行较高订单改进的Beran(1987、1988年)预示法(1987、1988年),通过将原始“靴杆杆”p值转换成“无症状”统一的随机变量,恢复了“靴杆”有效性。我们建议采用两种不同的预测(插座和双靴陷阱),并提供表明“靴杆”推断有效性的一般高层次条件。为了说明我们结果的实际相关性和执行情况,我们讨论了五项应用:(一) i.d.d.数据的简单位置模型,可能存在无限差异;(二) 带有省略控制的回归模型;(三) 基于模型平均值的目标参数的推断;(四) 脊柱型常规估计器;以及(五) 动态面板数据模型。