Testing normality of a large number of populations

Jiménez-Gamero, M. D.

doi:10.1007/s00362-022-01384-y

Cited by 3 publications

(1 citation statement)

References 32 publications

(38 reference statements)

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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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Testing Poissonity of a large number of populations

Jiménez-Gamero,

de Uña-Álvarez

2023

TEST

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This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws. The means of those populations may differ. The proposed procedure is designed for large k, which can be bigger than the sample sizes. First, a test is proposed for the case of independent samples, and then the obtained results are extended to dependent data. In each case, the asymptotic distribution of the test statistic is stated under the null hypothesis as well as under alternatives, which allows 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 is studied via simulation. A real data set application is included.

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