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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:185

Article

Dolores Jimenez-Gamero, M.¹  Franco-Pereira, Alba M.² 

[1] Univ Seville, Dept Estadist & Invest Operat, Seville, Spain

[2] Univ Complutense Madrid, Dept Estadist & Invest Operat, Madrid, Spain

关键词: Asymptotic normality;    Consistency;    Finite dimensional data;    Functional data;    Testing the equality of means;   

DOI  :  10.1016/j.jmva.2021.104778

来源: Elsevier

【 摘 要 】

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. (C) 2021 The Author(s). Published by Elsevier Inc.

【 授权许可】

Free