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Open AccessFeature PaperArticle
Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices
by
Yehenew G. Kifle
Yehenew G. Kifle 1
,
Alain M. Moluh
Alain M. Moluh 2 and
Bimal K. Sinha
Bimal K. Sinha 1,3,*
1
Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
2
United States Department of Agriculture, 5601 Sunnyside Ave, Beltsville, MD 20705, USA
3
Center for Statistical Research and Methodology, U.S. Census Bureau, 4600 Silver Hill Rd., Suitland-Silver Hill, MD 20746, USA
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(17), 2723; https://doi.org/10.3390/math12172723 (registering DOI)
Submission received: 5 July 2024
/
Revised: 21 August 2024
/
Accepted: 28 August 2024
/
Published: 31 August 2024
Abstract
This paper addresses the problem of making inferences about a common mean vector from several independent multivariate normal populations with unknown and unequal dispersion matrices. We propose an unbiased estimator of the common mean vector, along with its asymptotic estimated variance, which can be used to test hypotheses and construct confidence ellipsoids, both of which are valid for large samples. Additionally, we discuss an approximate method based on generalized p-values. The paper also presents exact test procedures and methods for constructing exact confidence sets for the common mean vector, with a comparison of the local power of these exact tests. The performance of the proposed methods is demonstrated through a simulation study and an application to data from the Current Population Survey (CPS) Annual Social and Economic (ASEC) Supplement 2021 conducted by the U.S. Census Bureau for the Bureau of Labor Statistics.
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MDPI and ACS Style
Kifle, Y.G.; Moluh, A.M.; Sinha, B.K.
Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices. Mathematics 2024, 12, 2723.
https://doi.org/10.3390/math12172723
AMA Style
Kifle YG, Moluh AM, Sinha BK.
Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices. Mathematics. 2024; 12(17):2723.
https://doi.org/10.3390/math12172723
Chicago/Turabian Style
Kifle, Yehenew G., Alain M. Moluh, and Bimal K. Sinha.
2024. "Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices" Mathematics 12, no. 17: 2723.
https://doi.org/10.3390/math12172723
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