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Abstract:
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Functional depth can order functional data from the center outwards. Although the prerequisite for applying current functional depths is that all functional data should be observed at the same time grids, missing values and outliers are frequently encountered in functional data. We approach these problems by inputting the missing values before applying functional depth. We build a general framework for multivariate functional data, where complete functional data are a particular case. Our simulation study covers different sparsity and outlier scenarios in multivariate functional data, and compares our method with two commonly discussed methods: FPCA applied marginally to each variable and conventional MFPCA. Based on the MFPCA approach, the completed multivariate functional data can then be ranked and visualized with the functional boxplot. We can use a magnitude-shape (MS) plot to make outliers detection possible for incomplete functional data. Numerical results together with a case study indicate that these visualization tools based on functional depth, coupled with the proposed missing value inputation method, can perform well.
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