Classification into two Multivariate Normal Distributions with Different Covariance Matrices

1962/06/01 by T. W. Anderson, R. R. Bahadur · 5 citations
Mathematics · Engineering · Decision Sciences · #Advanced Statistical Methods and Models #Fault Detection and Control Systems #Advanced Statistical Process Monitoring

paper · pdf · doi:10.1214/aoms/1177704568

Abstract

Linear procedures for classifying an observation as coming from one of two multivariate normal distributions are studied in the case that the two distributions differ both in mean vectors and covariance matrices. We find the class of admissible linear procedures, which is the minimal complete class of linear procedures. It is shown how to construct the linear procedure which minimizes one probability of misclassification given the other and how to obtain the minimax linear procedure; Bayes linear procedures are also discussed.

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