论文标题
从离散采样的功能数据中对位置的最佳估计进行了强大的最佳估计
Robust optimal estimation of location from discretely sampled functional data
论文作者
论文摘要
估计位置是功能数据分析的中心问题，但是大多数当前的估计程序要么不切实际地假设完全观察到的轨迹或缺乏相对于在功能环境中遇到的多种异常情况的鲁棒性。为了解决这些缺陷，我们基于离散采样的功能数据介绍了第一类最佳鲁棒位置估计器。所提出的方法是基于M型平滑样条估计，并重复测量，适用于常见和独立观察到的轨迹，这些轨迹可能会遇到测量误差。我们表明，在适当的假设下，提出的估计量家族是通常和独立观察到的轨迹的最低率率，我们在蒙特 - 卡洛研究中说明了其高度竞争性的性能和实用性，以及涉及最近Covid-19的数据的真实数据示例。
Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one can encounter in the functional setting. To remedy these deficiencies we introduce the first class of optimal robust location estimators based on discretely sampled functional data. The proposed method is based on M-type smoothing spline estimation with repeated measurements and is suitable for both commonly and independently observed trajectories that are subject to measurement error. We show that under suitable assumptions the proposed family of estimators is minimax rate optimal both for commonly and independently observed trajectories and we illustrate its highly competitive performance and practical usefulness in a Monte-Carlo study and a real-data example involving recent Covid-19 data.
