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Abstract:
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There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation depth, for functional data. As a measure of depth, its properties are studied theoretically, and the outlier detection performance is investigated through simulations. Compared to magnitude outliers, shape outliers are often masked among the rest of samples and more difficult to identify. We show that the proposed depth measure has many desirable features and is well suited for shape outlier detection due to the fact that it considers the total variation in the functional data and takes into account the necessary correlations. Effective tools for visualizing shape outliers are also developed and illustrated through real data examples.
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