Two-sample test on funscalar data with application to hemodialysis monitoring by Raman spectroscopy
To achieve in-session monitoring of hemodialysis through Raman spectroscopy, it is necessary to compare data consist of Raman spectra and intensity values for specific biomarkers (e.g., urea) contained in waste dialysate used in hemodialysis treatement. This calls for the development of a two-sample test procedure for funscalar data, data that are a mix of functional and scalar variables. Despite a rich literature on univariate functional data testing procedures and a few publications on multivariate functional data testing procedures, there is no such a testing procedure for funscalar data. In this work we propose the first testing procedure for funscalar data, generalizing the functional data approach in Horvath et al (2013). The test statistic is based on the L_2 distance between the two mean funscalar objects. Its asymptotic null distribution and asymptotic power are studied. We then demonstrate its performance through extensive simulations and its usefulness is through data collected in our hemodialysis monitoring experiments.
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