Testing the equality of a large number of means of functional data
| Autor: | M. Dolores Jiménez-Gamero, Alba M. Franco-Pereira |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Numerical Analysis education.field_of_study Population Asymptotic distribution 020206 networking & telecommunications Estadística 02 engineering and technology 01 natural sciences 010104 statistics & probability Consistency (statistics) Sample size determination Bounded function 0202 electrical engineering electronic engineering information engineering Null distribution Test statistic Applied mathematics 0101 mathematics Statistics Probability and Uncertainty education Null hypothesis Mathematics |
| Zdroj: | E-Prints Complutense. Archivo Institucional de la UCM instname |
| ISSN: | 0047-259X |
| DOI: | 10.1016/j.jmva.2021.104778 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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