Optimum Classification Rules for Classification into Two Multivariate Normal Populations

摘要

It is shown that the maximum likelihood classification rule is unbiased, admissible and minimax when the common covariance matrix of the two normal propulations is known and when the common covariance matrix is unknown, the corresponding maximum likelihood rule is unbiased and in an invariant class it is also minimax and admissible. The loss function in each problem is assumed to be a function (satisfying some mild restrictions) of the Mahalanobis distance between the two populations.