Abstract
Given k independent samples with finite but arbitrary dimension, this paper deals with the problem of testing for the equality of their distributions that can be continuous, discrete or mixed. In contrast to the classical setting where k is assumed to be fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample is either bounded or small in comparison with k. The asymptotic distribution of two test statistics is stated under the null hypothesis of the equality of the k distributions as well as under alternatives, which let us to study the asymptotic power of the resulting tests. Specifically, it is shown that both test statistics are asymptotically free distributed under the null hypothesis. The finite sample performance of the tests based on the asymptotic null distribution is studied via simulation. An application of the proposal to a real data set is included. The use of the proposed procedure for infinite dimensional data, as well as other possible extensions, are discussed.
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Acknowledgements
The authors thank the Associate Editor and two anonymous referees for their constructive comments and suggestions which helped to improve the presentation. M.D. Jiménez-Gamero has been partially supported by Grants MTM2017-89422-P (Spanish Ministry of Economy, Industry and Competitiveness, the State Agency of Investigation, the European Regional Development Fund) and P18-FR-2369 (Junta de Andalucía). M. Cousido-Rocha has received financial support of SiDOR research group through the Grant Competitive Reference Group, 2016-2019 (ED431C 2016/040), funded by the Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia, also by Grant MTM2017-89422-P. M.V. Alba-Fernández and F. Jiménez-Jiménez acknowledge the financial support provided by the Grant EI_SEJ5_2019 (Universidad de Jaén).
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Jiménez-Gamero, M.D., Cousido-Rocha, M., Alba-Fernández, M.V. et al. Testing the equality of a large number of populations. TEST 31, 1–21 (2022). https://doi.org/10.1007/s11749-021-00769-9
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DOI: https://doi.org/10.1007/s11749-021-00769-9