RT Journal Article
T1 A consistent test of equality of distributions for Hilbert-valued random elements
A1 González Rodríguez, Gil
A1 Colubi Cervero, Ana
A1 González-Manteiga, Wenceslao
A1 Febrero Bande, Manuel
K1 Bootstrap method
K1 Consistency
K1 Functional data
K1 Hypothesis testing
K1 Separable Hilbert spaces
AB Two independent random elements taking values in a separable Hilbert space are considered.The aim is to develop a test with bootstrap calibration to check whether they have the samedistribution or not. A transformation of both random elements into a new separable Hilbertspace is considered so that the equality of expectations of the transformed random elements isequivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equalityof means can be used in order to solve the original problem. It will be shown that both theasymptotic and bootstrap approaches proposed are asymptotically correct and consistent. Theresults can be applied, for example, in functional data analysis. In practice, the test can be solvedwith simple operations in the original space without applying the mentioned transformation,which is used only to guarantee the theoretical results. Empirical results and comparisons withrelated methods support and complement the theory.
PB Elsevier
SN 0047-259X
YR 2024
FD 2024
LK http://hdl.handle.net/10347/33344
UL http://hdl.handle.net/10347/33344
LA eng
NO González–Rodríguez G, Colubi A, González–Manteiga W, Febrero–Bande M (2024). A consistent test of equality of distributions for Hilbert-valued random elements. Journal of Multivariate Analysis, Volume 202, 105312. ISSN 0047-259X. https://doi.org/10.1016/j.jmva.2024.105312
NO The research has been partially supported by Grants MTM2017-89632-P and PID2020-116587GB-I00 funded byMICIU/AEI/10.13039/501100011033 and the COST Action CA21163 from the European Cooperation in Science and Technology. The authors would like to express their gratitude to the referees and editors by their helpful comments and suggestions.
DS Minerva
RD 24 abr 2026