Testing the equality of a large number of means of functional data



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Jiménez-Gamero, M. Dolores and Franco Pereira, Alba M. (2021) Testing the equality of a large number of means of functional data. Journal of multivariate analysis, 185 . p. 104778. ISSN 0047-259X

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Official URL: https://doi.org/10.1016/j.jmva.2021.104778


Given k independent samples of functional data, this paper deals with the problem of testing for the equality of their mean functions. In contrast to the classical setting, where k is kept 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 to k. A new test is proposed. The asymptotic distribution of the test statistic is stated under the null hypothesis of equality of the k mean functions as well as under alternatives, which allows us to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. The finite sample performance of the test based on the asymptotic null distribution is studied via simulation. Although we start by assuming that the data are functions, the proposed test can also be applied to finite dimensional data. The practical behavior of the test for one dimensional data is numerically studied and compared with other tests.

Item Type:Article
Additional Information:

CRUE-CSIC (Acuerdos Transformativos 2021)

Uncontrolled Keywords:Asymptotic normality, Consistency, Finite dimensional data, Functional data, Testing the equality of means
Subjects:Sciences > Statistics
ID Code:70063
Deposited On:04 Feb 2022 14:31
Last Modified:18 Oct 2022 09:06

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