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Title: Application of functional correlation in biology and econometrics Authors:  Christian Ritz - University of Copenhagen (Denmark) [presenting]
Anne van Delft - Columbia University (United States)
Abstract: In much applied, exploratory research correlation coefficients are used as a means for gauging the strength of relationships between different outcomes or responses measured or recorded on the same entities, subject, or units, repeatedly over time. These coefficients may be indicative of presence or absence of an association or linkage between underlying mechanisms or processes, e.g., test of independence. Both within biology and econometrics data are typically unbalanced, either rich or sparse, and it remains challenging to provide describe such data in terms of standard statistical models. For instance, standard Pearson or Spearman correlation coefficients may be calculated between pairs of responses for each time point or for all time points pooled. In both cases dependencies over time are not taken into account. However, these data fit perfectly within the framework of functional data and functional data methods seem well suited for analyzing such data. Recently, a functional correlation coefficient was proposed using singular value decompositions. The aim of the present study is to further demonstrate the usefulness of the functional correlation coefficient. To our knowledge the concept of a functional correlation coefficient has not so far been utilized in biology and econometrics in any noticeable extent.