Testing the equality of estimable parameters across many populations

Fuente: arXiv
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Main Authors: Romero-Madroñal, Marcos, Sillero-Denamiel, María de los Remedios, Jiménez-Gamero, María Dolores
Format: Preprint
Published: 2025
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author Romero-Madroñal, Marcos
Sillero-Denamiel, María de los Remedios
Jiménez-Gamero, María Dolores
author_facet Romero-Madroñal, Marcos
Sillero-Denamiel, María de los Remedios
Jiménez-Gamero, María Dolores
contents The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that samples with increasing sample sizes are available from each population. This paper introduces and studies a test for the comparison of an estimable parameter across $k$ populations, when $k$ is large and the sample sizes from each population are small when compared with $k$. The proposed test statistic is asymptotically distribution-free under the null hypothesis of parameter homogeneity, enabling asymptotically exact inference without parametric assumptions. Additionally, the behaviour of the proposal is studied under alternatives. Simulations are conducted to evaluate its finite-sample performance, and a linear bootstrap method is implemented to improve its behaviour for small $k$. Finally, an application to a real dataset is presented.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06763
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Testing the equality of estimable parameters across many populations
Romero-Madroñal, Marcos
Sillero-Denamiel, María de los Remedios
Jiménez-Gamero, María Dolores
Statistics Theory
Methodology
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that samples with increasing sample sizes are available from each population. This paper introduces and studies a test for the comparison of an estimable parameter across $k$ populations, when $k$ is large and the sample sizes from each population are small when compared with $k$. The proposed test statistic is asymptotically distribution-free under the null hypothesis of parameter homogeneity, enabling asymptotically exact inference without parametric assumptions. Additionally, the behaviour of the proposal is studied under alternatives. Simulations are conducted to evaluate its finite-sample performance, and a linear bootstrap method is implemented to improve its behaviour for small $k$. Finally, an application to a real dataset is presented.
title Testing the equality of estimable parameters across many populations
topic Statistics Theory
Methodology
url https://arxiv.org/abs/2510.06763