Inference About a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices
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Type of Work37 pages
Citation of Original PublicationKifle, Yehenew G., Alain M. Moluh and Bimal K. Sinha. "Inference About a Common Mean Vector from Several Independent Multinormal Populations with Unequal and Unknown Dispersion Matrices." United States Census Bureau (AUGUST 22, 2022). https://www.census.gov/library/working-papers/2022/adrm/RRS2022-04.html
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In this paper we consider the problem of drawing inference about a common mean vector based on data from several independent multivariate normal populations with unknown and unequal dispersion matrices. An unbiased estimate of the common mean vector with its asymptotic estimated variance is suggested to test a hypothesis about it and also to construct a confidence ellipsoid. Both are valid in large samples. Another approximate method based on the notion of generalized P-value is also mentioned. Exact test procedures and construction of exact confidence sets for the common mean vector are presented. A comparison of the exact tests based on their local power is carried out. Applications include a simulated data set and also data from Current Population Survey (CPS) Annual Social and Economic Supplement (ASEC) 2021, conducted by the US Bureau of the Census for the Bureau of Labor Statistics.
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