Robust methods for functional data analysis

功能数据和其他复杂类型的数据出现在许多不同的应用程序中。我对这个话题的兴趣是由美国科罗拉多州国家大气研究中心（NCAR）的研究人员提请我们注意的一个问题引起的。他们的目标是识别气象气球记录的潜在的非典型（或偏远）观测结果。考虑到大量的可用记录（约3000万），无监督异常值检测方法将特别有用。基于到“中心”（或其他“中间”类型代表）的距离来检测异常值的多变量方法很难扩展到功能数据，因为在许多情况下，如何标准化这些距离以获得适当的阈值并不清楚。受可用数据的特征（特别是它们的稀疏性）的激励，我将研究基于观察曲线和预测曲线之间距离的异常值检测方法。所提出的方法在概念上不同于以前的建议，因为它不需要对协方差函数进行稳健估计。

Functional and other complex types of data arise in a number of different applications. My interest in this topic is motivated by a problem brought to our attention by researchers at the National Centre for Atmospheric Research (NCAR) in Colorado, USA. Their goal is to identify potentially atypical (or outlying) observations recorded by weather balloons. Given the large number of records available (~30 million), unsupervised outlier detection methods would be particularly useful. Multivariate methods to detect outliers based on distances to the "centre" (or other "medoid"-type representative) are difficult to extend to functional data because in many cases it is not clear how to standardize these distances in order to obtain an appropriate threshold. Motivated by the characteristics of the available data (particularly their sparsity), I will investigate outlier detection methods based on distances between observed and predicted curves. The proposed approach is conceptually different from previous proposals in that it is not necessary to estimate robustly the covariance function.