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Rank tests for functional data based on the epigraph, the hypograph and associated graphical representations

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Abstract

Visualization techniques are very useful in data analysis. Their aim is to summarize information into a graph or a plot. In particular, visualization is especially interesting when one has functional data, where there is no total order between the data of a sample. Taking into account the information provided by the down–upward partial orderings based on the hypograph and the epigragh indexes, we propose new strategies to analyze graphically functional data. In particular, combining the two indexes we get an alternative way to measure centrality in a bunch of curves, so we get an alternative measure to the statistical depth. Besides, motivated by the visualization in the plane of the two measures for two functional data samples, we propose new methods for testing homogeneity between two groups of functions. The performance of the tests is evaluated through a simulation study and we have applied them to several real data sets.

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Acknowledgements

This work has received financial support from the project MTM2017-89422-P of the Spanish Ministry of Economy and Competitiveness, the Xunta de Galicia (Centro singular de investigación de Galicia accreditation 2016–2019) and the European Union (European Regional Development Fund—ERDF). We also acknowledge support from the project ECO2015-66593-P of the Spanish Ministry of Science and Technology.

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Authors and Affiliations

  1. Department of Statistics and OR, Complutense University of Madrid, Plaza de Ciencias 3, 28040, Madrid, Spain

    Alba M. Franco-Pereira

  2. UC3M-Santander Big Data Institute, Universidad Carlos III de Madrid, Getafe, Madrid, Spain

    Alba M. Franco-Pereira & Rosa E. Lillo

  3. Department of Statistics, Carlos III University of Madrid, C/Madrid, 126, 28903, Getafe, Madrid, Spain

    Rosa E. Lillo

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  1. Alba M. Franco-Pereira
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  2. Rosa E. Lillo
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Correspondence to Alba M. Franco-Pereira.

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Franco-Pereira, A.M., Lillo, R.E. Rank tests for functional data based on the epigraph, the hypograph and associated graphical representations. Adv Data Anal Classif 14, 651–676 (2020). https://doi.org/10.1007/s11634-019-00380-9

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