论文标题
Smoothem：一种同时评估平滑模式和尖峰的新方法
smoothEM: a new approach for the simultaneous assessment of smooth patterns and spikes
论文作者
论文摘要
我们考虑了功能数据，其中基础平滑曲线不仅与错误组成，而且还与不规则的尖峰组成。我们提出了一种方法，该方法将正则化样条平滑和一种期望最大化算法相结合，使人们可以识别尖峰并估算平滑分量。对错误分布施加了一些假设，我们证明了EM估计值的一致性。接下来，我们证明了我们关于有限样本的提议的表现及其对通过模拟违规假设的鲁棒性。最后，我们将建议应用于美国的年度热浪指数以及爱尔兰的每周电力消耗。在两个数据集中，我们都能够表征基本的平稳趋势，并确定不规则/极端行为。
We consider functional data where an underlying smooth curve is composed not just with errors, but also with irregular spikes. We propose an approach that, combining regularized spline smoothing and an Expectation-Maximization algorithm, allows one to both identify spikes and estimate the smooth component. Imposing some assumptions on the error distribution, we prove consistency of EM estimates. Next, we demonstrate the performance of our proposal on finite samples and its robustness to assumptions violations through simulations. Finally, we apply our proposal to data on the annual heatwaves index in the US and on weekly electricity consumption in Ireland. In both datasets, we are able to characterize underlying smooth trends and to pinpoint irregular/extreme behaviors.
