We propose a weighted bootstrap approach that can improve on current methods to approximate the finite sample distribution of normalized maximal deviations of kernel deconvolution density estimators in the case of ordinary smooth errors. Using results from the approximation theory for weighted bootstrap empirical processes, we establish an unconditional weak limit theorem for the corresponding weighted bootstrap statistics. Because the proposed method uses weights that are not necessarily confined to be uniform (as in Efron’s original bootstrap), it provides the practitioner with additional flexibility for choosing the weights. As an immediate consequence of our results, one can construct uniform confidence bands, or perform goodness-of-fit tests, for the underlying density. We have also carried out some numerical examples which show that, depending on the bootstrap weights chosen, the proposed method has the potential to perform better than the current procedures in the literature.

中文翻译：

---

关于加权自举核反卷积密度估计器的性能

我们提出了一种加权自举方法，该方法可以改进当前方法，以在普通平滑误差的情况下近似核反卷积密度估计器的归一化最大偏差的有限样本分布。使用加权自举经验过程的近似理论的结果，我们为相应的加权自举统计建立了无条件弱极限定理。因为所提出的方法使用不一定限于统一的权重（如在 Efron 的原始引导程序中），它为从业者提供了选择权重的额外灵活性。作为我们结果的直接结果，人们可以为基础密度构建统一的置信带，或执行拟合优度测试。我们还进行了一些数值例子，表明，