Testing the equality of a large number of populations

Jiménez-Gamero, M. D.; Cousido‐Rocha, Marta; Alba-Fernández, V.; Jiménez-Jiménez, Francisca

doi:10.1007/s11749-021-00769-9

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…The reason to opt for the sum is that, under the null hypothesis, we get an asymptotic free distributed test statistic (as shown in Corollary 1). The same is observed in other sum‐type test statistics as those in Park and Park (2012), Zhan and Hart (2014), Jiménez‐Gamero and Franco‐Pereira (2021), Jiménez‐Gamero et al (2022) and Jiménez‐Gamero (2023), just to cite a few. If one instead takes the maximum, the asymptotic null distribution of the resultant test statistic becomes more complicated, and one has to resort to resampling in order to approximate its null distribution.…”

Section: The Test Statisticsupporting

confidence: 68%

Homogeneity of marginal distributions for a large number of populations

Alba‐Fernández,

Jiménez‐Gamero

2023

Stat

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SummaryAssume that a random vector is observed in populations and independent samples of that random vector are available at each population. Assume that and have the same dimension. Our purpose is to test the equality of the marginal distributions of and in the populations when is large compared to the sample sizes. With this aim, we propose and study a test statistic that compares the empirical characteristic functions of the marginal distributions. Under the null, the test statistic is asymptotically free‐distributed. An expression of the asymptotic power is also derived, which allows to study the consistency of the test. No assumption is made on the distribution of and , which can be continuous, discrete or mixed; moreover, no assumption is made about moments. A simulation study investigates the finite sample performance of the new test. The proposal is applied to study air pollution levels that are directly related to environmental health, in all countries where observations are available.

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Section: The Test Statisticsupporting

confidence: 68%

Homogeneity of marginal distributions for a large number of populations

Alba‐Fernández,

Jiménez‐Gamero

2023

Stat

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“…Nevertheless, the efficiency of those procedures may decrease, or even disappear, if the normality assumption fails. For example, if one can assume that the populations are normal, then the classical k-sample problem becomes that of testing the equality of variances and the equality of means, for which more tests can be found in the statistical literature than for testing the equality of the k distributions when k is large (Zhan and Hart 2014;Jiménez-Gamero et al 2022). As another instance, let us consider the problem of testing the equality of the means of a large number k of univariate normal populations, that may have different variances.…”

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confidence: 99%

Testing normality of a large number of populations

Jiménez-Gamero

2023

Stat Papers

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“…The more complex problem of testing the equality of a large number of populations has been recently studied in Jiménez-Gamero et al. ( 2022 ). Motivated by biomechanical studies where the aim is to test the differences between the means of the human movement curves observed on independent samples of subjects under different treatments, the current manuscript is focused on addressing this tool from a Functional Data Analysis (FDA) perspective.…”

Section: Introductionmentioning

confidence: 99%

Basis expansion approaches for functional analysis of variance with repeated measures

Acal

Aguilera

2022

Adv Data Anal Classif

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The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many cases the aim consists of detecting differences in gait patterns when several independent samples of subjects walk or run under different conditions (repeated measures). Classic kinematic studies often analyse discrete summaries of the sample curves discarding important information and providing biased results. As the sample data are obviously curves, a Functional Data Analysis approach is proposed to solve the problem of testing the equality of the mean curves of a functional variable observed on several independent groups under different treatments or time periods. A novel approach for Functional Analysis of Variance (FANOVA) for repeated measures that takes into account the complete curves is introduced. By assuming a basis expansion for each sample curve, two-way FANOVA problem is reduced to Multivariate ANOVA for the multivariate response of basis coefficients. Then, two different approaches for MANOVA with repeated measures are considered. Besides, an extensive simulation study is developed to check their performance. Finally, two applications with gait data are developed.

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Testing the equality of a large number of populations

Cited by 6 publications

References 20 publications

Homogeneity of marginal distributions for a large number of populations

Homogeneity of marginal distributions for a large number of populations

Testing normality of a large number of populations

Basis expansion approaches for functional analysis of variance with repeated measures

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