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Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices

Author

Listed:
  • Yehenew G. Kifle

    (Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA)

  • Alain M. Moluh

    (United States Department of Agriculture, 5601 Sunnyside Ave, Beltsville, MD 20705, USA)

  • Bimal K. Sinha

    (Department of Mathematics and Statistics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
    Center for Statistical Research and Methodology, U.S. Census Bureau, 4600 Silver Hill Rd., Suitland-Silver Hill, MD 20746, USA)

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.

Suggested Citation

  • Yehenew G. Kifle & Alain M. Moluh & Bimal K. Sinha, 2024. "Inference about a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices," Mathematics, MDPI, vol. 12(17), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2723-:d:1468447
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