Publication: Spearman coefficient for functions
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2013-12
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Abstract
We present a notion of Spearman's coefficient for functional data that
extends the classical bivariate concept to situations where the observed data
are curves generated by a stochastic process. Since Spearman's coefficient
for bivariate samples is based on the natural data ordering in dimension
one, we need to consider a data order in the functional context where a
natural order between functions does not exist. The development uses a
pre-order inspired in a depth definition but considering a down-up ordering
instead of a center-outwards ordering of the sample. We show some of the
main characteristics of Spearman's coefficient for functions and propose an
independence test with a bootstrap methodology. We illustrate the
performance of the new coefficient with both simulated and real data
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Keywords
Spearman's coefficient;, Dependence, Functional data, Grades