Homogeneity of marginal distributions for a large number of populations

Summary Assume that a random vector (X,Y) is observed in k populations and independent samples of that random vector are available at each population. Assume that X and Y have the same dimension. Our purpose is to test the equality of the marginal distributions of X and Y in the k populations when k...

Full description

Saved in:
Bibliographic Details
Published in:Stat (International Statistical Institute) 2023-01, Vol.12 (1), p.n/a
Main Authors: Alba‐Fernández, M. V., Jiménez‐Gamero, M. D.
Format: Article
Language:English
Subjects:
asymptotic properties
many subpopulations
paired data
two‐sample problem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Summary Assume that a random vector (X,Y) is observed in k populations and independent samples of that random vector are available at each population. Assume that X and Y have the same dimension. Our purpose is to test the equality of the marginal distributions of X and Y in the k populations when k 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 X and Y, 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.
ISSN:2049-1573
2049-1573
DOI:10.1002/sta4.617