Abstract
When a (p+q)-variate column vector (x′,y′)′ has a (p+q)-variate normal density with mean vector (μ1,μ2) and covariance matrix Ω, unknown, Schervish (1980) obtains prediction intervals for the linear functions of a future y, given x. He bases the prediction interval on the F-distribution. However, for a specified linear function the statistic to be used is Student's t, since the prediction intervals based on t are shorter than those based on F. Similar results hold for the multivariate linear regression model.
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Scheffe, H. (1959).The Analysis of Variance, Wiley and Sons, New York.
Schervish, Mark J. (1980). Tolerance regions for random vectors and best linear predictors.Commun. Statist. Theory Meth. A9, 1177–1183.
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Kabe, D.G., Gupta, A.K. A note on tolerance regions for random vectors and best linear predictors. Statistical Papers 31, 285–289 (1990). https://doi.org/10.1007/BF02924701
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DOI: https://doi.org/10.1007/BF02924701