论文标题
通过应用在线曲线估计，了解嘈杂曲线的平稳性
Learning the smoothness of noisy curves with application to online curve estimation
论文作者
论文摘要
结合轨迹内部和跨越轨迹的信息，我们为随机过程的轨迹局部规律性提出了一个简单的估计器。在随机采样时间点以误差测量独立轨迹。得出了估计量浓度的非反应界限。鉴于局部规律性的估计，我们从新的，可能是非常大的嘈杂轨迹样本的曲线中构建了一个几乎最佳的局部多项式更加顺畅。我们在新的曲线集中均匀地得出了非反应的尖端风险界限。我们的估计在模拟中表现良好。实际数据集说明了新方法的有效性。
Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time points. Non-asymptotic bounds for the concentration of the estimator are derived. Given the estimate of the local regularity, we build a nearly optimal local polynomial smoother from the curves from a new, possibly very large sample of noisy trajectories. We derive non-asymptotic pointwise risk bounds uniformly over the new set of curves. Our estimates perform well in simulations. Real data sets illustrate the effectiveness of the new approaches.
