Sign and signed rank tests for paired functions

Abstract: Simple nonparametric tests for paired functional data are an understudied area, despite recent advances in similar tests for other types of functional data. While the sign test has received limited treatment, the signed rank-type test has not previously been examined. The aim of the present work is to develop and evaluate these types of tests for functional data. We derive a simple, theoretical framework for both sign and signed rank tests for pairs of functions. In particular, we demonstrate that doubly ranked testing -- a newly developed framework for testing hypotheses involving functional data -- is a useful conduit for examining hypotheses regarding pairs o,f functions. We briefly examine the operating characteristics of all derived tests. We also use the described approaches to re-analyze pairs of functions from a randomized crossover study of heart health during simulated flight.