Robust methods for functional data analysis

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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.