Inference methods for computing confidence intervals in parametric settings usually rely on consistent estimators of the parameter of interest. However, it may be computationally and/or analytically burdensome to obtain such estimators in various parametric settings, for example when the data exhibit certain features such as censoring, misclassification errors or outliers. To address these challenges, we propose a simulation-based inferential method, called the implicit bootstrap, that remains valid regardless of the potential asymptotic bias of the estimator on which the method is based. We demonstrate that this method allows for the construction of asymptotically valid percentile confidence intervals of the parameter of interest. Additionally, we show that these confidence intervals can also achieve second-order accuracy. We also show that the method is exact in three instances where the standard bootstrap fails. Using simulation studies, we illustrate the coverage accuracy of the method in three examples where standard parametric bootstrap procedures are computationally intensive and less accurate in finite samples.

翻译：在参数化设定中计算置信区间的推断方法通常依赖于对目标参数的一致估计量。然而，在各种参数化设定中（例如当数据呈现截尾、误分类误差或异常值等特定特征时），获得此类估计量可能在计算和/或分析上较为困难。为应对这些挑战，我们提出一种基于模拟的推断方法，称为隐式自助法，该方法无论其基础估计量是否存在潜在的渐近偏差均保持有效性。我们证明该方法能够为目标参数构建渐近有效的百分位置信区间。此外，我们还表明这些置信区间同样可以达到二阶精度。我们进一步证明该方法在标准自助法失效的三种情形下具有精确性。通过模拟研究，我们在三个示例中展示了该方法的覆盖精度，这些示例中标准参数自助法程序计算密集且在有限样本中精度较低。