Statistical Papers

, Volume 31, Issue 1, pp 285–289 | Cite as

A note on tolerance regions for random vectors and best linear predictors

  • D. G. Kabe
  • A. K. Gupta


When a (p+q)-variate column vector (x′,y′)′ has a (p+q)-variate normal density with mean vector (μ12) 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.


Linear Regression Model Prediction Interval Joint Density Multivariate Linear Regression Model Prediction Region 
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  1. Scheffe, H. (1959).The Analysis of Variance, Wiley and Sons, New York.MATHGoogle Scholar
  2. Schervish, Mark J. (1980). Tolerance regions for random vectors and best linear predictors.Commun. Statist. Theory Meth. A9, 1177–1183.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • D. G. Kabe
    • 1
  • A. K. Gupta
    • 2
  1. 1.Department of MathematicsSt. Mary's UniversityHalifaxCanada
  2. 2.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA

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