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Title: Comparing paired distributions using a functional data approach Authors:  Anne Gegout-Petit - INRIA Universite de Lorraine-IECL BIGS (France)
Juhyun Park - ENSIIE (France) [presenting]
Abstract: A paired hypothesis testing problem arises when the same variable of interest is measured before and after a treatment is applied. We are interested in the case where we only have access to a summary measure in terms of distribution functions of a common random variable. Hence the treatment effect is assumed to be reflected in the change in the distribution functions. Although the data as distribution functions could be viewed as instances of functional data, the standard testing framework based on the mean change in an $L_2$ Hilbert space poses several difficulties due to the inherent constraints on the distribution functions. Instead, we propose to measure a nonlinear change by means of a warping function between the paired distribution functions and formulate a one-sample hypothesis testing problem based on the median of the warping functions. In order to properly define a functional median, we equip the space of warping functions with a transformation induced norm and define a hypothesis using a norm-based geometric median. A version of a permutation test and an asymptotic test are developed, and their performance is compared with both simulation studies and a real data example.