A Selection Procedure for Multivariate Normal Distributions in Terms of the Generalized Variances

The present paper discusses some ranking and selection procedures for multivariate normal populations in terms of measures of dispersion. Using the generalized variance as the measure of dispersion, a procedure is defined to select a subset of the populations which would include the population with the smallest generalized variance with a certain probability. Two approximations to the distribution of the sample generalized variance are discussed. A discussion of the properties of the above procedure is also included.