Abstract:
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In functional data analysis, data depth provides a robust way of summarizing the distribution of functional data and, detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal depth, are constructed from pointwise depth for each observed functional observation. Instead of calculating one single depth value for each functional observation, this article proposes the use of the distribution of the pointwise depth for magnitude outlier detection and the correlation between pairwise depth for shape outlier detection. We also develop a bootstrap-based testing procedure for the correlation to test whether there is any shape outlier. The proposed methods are then extended to bivariate functional data. We evaluate the performance of the proposed methods by simulations under various outlier models. Finally, we demonstrate the developed visualization and outlier detection tools by real data applications. We illustrate the procedure by detecting outliers in a dataset of system power (PV), Global Solar Irradiance (SI), and Sun Height (SH) taken from a KAUST station in Saudi Arabia.
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