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A Kendall correlation coefficient between functional data. (English) Zbl 1459.62092

Summary: Measuring dependence is a very important tool to analyze pairs of functional data. The coefficients currently available to quantify association between two sets of curves show a non robust behavior under the presence of outliers. We propose a new robust numerical measure of association for bivariate functional data. We extend in this paper Kendall coefficient for finite dimensional observations to the functional setting. We also study its statistical properties. An extensive simulation study shows the good behavior of this new measure for different types of functional data. Moreover, we apply it to establish association for real data, including microarrays time series in genetics.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62H25 Factor analysis and principal components; correspondence analysis
62R10 Functional data analysis

Software:

fda (R)
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References:

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