Confidence Regions for the Common Mean Vector of Several Multivariate Normal Populations

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Mathematics & Statistics


Suppose that there are independent samples available from several multivariate normal populations with the same mean vector m̈ but possibly different covariance matrices. The problem of developing a confidence region for the common mean vector based on all the samples is considered. An exact confidence region centered at a generalized version of the well‐known Graybill‐Deal estimator of m̈ is developed, and a multiple comparison procedure based on this confidence region is outlined. Necessary percentile points for constructing the confidence region are given for the two‐sample case. For more than two samples, a convenient method of approximating the percentile points is suggested. Also, a numerical example is presented to illustrate the methods. Further, for the bivariate case, the proposed confidence region and the ones based on individual samples are compared numerically with respect to their expected areas. The numerical results indicate that the new confidence region is preferable to the single‐sample versions for practical use. Copyright © 1995 Statistical Society of Canada



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Canadian Journal of Statistics

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