Title: Testing the equality of distributions of two independent Hilbert-valued random elements
Authors: Gil Gonzalez-Rodriguez - University of Oviedo (Spain) [presenting]
Ana Colubi - Justus Liebig University Giessen (Germany)
Wenceslao Gonzalez-Manteiga - University of Santiago de Compostela (Spain)
Manuel Febrero-Bande - University of Santiago de Compostela (Spain)
Abstract: The aim is to develop a bootstrap test to check whether two independent random elements taking on values in a separable Hilbert space have the same distribution or not. A transformation of both random elements into a new separable Hilbert space will be considered in such a way that the equality of expectations of the transformed random elements characterizes the equality of distributions. Consequently, any bootstrap procedure to check the equality of means of two independent random elements taking on values in a separable Hilbert space can be used to solve the original problem. This simple strategy is complemented by checking that the bootstrap procedure can be used without the need to transform the random elements, by applying some simple transformations in the original space.