标题： 未知误差分布的去卷积中的自适应分位数估计 显示英文标题

标题： Adaptive quantile estimation in deconvolution with unknown error distribution

摘要： 全面研究了deconvolution问题中的分位数估计。 特别地，涵盖了未知误差分布的更现实设定。 我们的插件方法基于一个deconvolution密度估计量，并在最小且自然的条件下达到minimax最优。 这填补了文献中的一个重要空白。 通过数据驱动的带宽选择获得了最优自适应估计。 作为副产品，我们得到了未知误差分布的插件分布函数估计的最优速率。 该方法被应用于一个真实数据实例。 显示英文摘要

摘要： Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result, we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.