Testing the equality of a large number of populations

• M. D. Jiménez-Gamero ^[1] ; M. Cousido-Rocha ^[2] ; M. V. Alba-Fernández ^[3] ; F. Jiménez-Jiménez ^[3]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  2. [2] Universidade de Vigo

     Universidade de Vigo

     Vigo, España

     
  3. [3] Universidad de Jaén

     Universidad de Jaén

     Jaén, España

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 1, 2022, págs. 1-21
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.