Depth measures for multivariate functional data. (English) Zbl 1347.62093

Summary: In this article, we address the problem of mining and analyzing multivariate functional data. That is, data where each observation is a set of possibly correlated functions. Complex data of this kind is more and more common in many research fields, particularly in the biomedical context. In this work, we propose and apply a new concept of depth measure for multivariate functional data. With this new depth measure it is possible to generalize robust statistics, such as the median, to the multivariate functional framework, which in turn allows the application of outlier detection, boxplots construction, and nonparametric tests also in this more general framework. We present an application to Electrocardiographic (ECG) signals.


62H15 Hypothesis testing in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C55 Biomedical imaging and signal processing
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[1] DOI: 10.1007/s00180-007-0053-0 · Zbl 1195.62032
[2] DOI: 10.1007/BF02595872 · Zbl 0942.62062
[3] DOI: 10.1007/BF02595706 · Zbl 1016.62026
[4] Ieva , F. ( 2011 ). Outlier detection for training sets in an unsupervised functional classification framework: An application to ECG signals.Proc. 17th EYSM.Portugal: Lisbon .
[5] Ieva F., J. Roy. Statist. Soc. Ser. C (Appl. Statist.). (2012)
[6] DOI: 10.1214/088342304000000594 · Zbl 1100.62564
[7] DOI: 10.1214/aos/1176347507 · Zbl 0701.62063
[8] Liu R., J. Amer. Statist. Assoc. 88 (421) pp 252– (1993)
[9] Lopez-Pintado S., Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications pp 103– (2006)
[10] DOI: 10.1016/j.csda.2006.10.029 · Zbl 1162.62359
[11] DOI: 10.1198/jasa.2009.0108 · Zbl 1388.62139
[12] Serfling R., Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications (2006)
[13] DOI: 10.1198/jcgs.2011.09224
[14] DOI: 10.1002/sta4.8
[15] Tukey J., Proc. 1975 Int. Congr. Math. 2 pp 523– (1975)
[16] DOI: 10.1214/aos/1016218226 · Zbl 1106.62334
[17] DOI: 10.1214/aos/1065705115 · Zbl 1046.62056
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