Empirical Bayes Posterior Odds Ratio for Heteroscedastic Classification

  • Kim, Hea-Jung (Department of Statistics, Dongguk University, Seoul 100)
  • 발행 : 1987.12.01

초록

Our interest is to access in some way teh relative odds or probability that a multivariate observation Z belongs to one of k multivariate normal populations with unequal covariance matrices. We derived the empirical Bayes posterior odds ratio for the classification rule when population parameters are unknown. It is a generalization of the posterior odds ratio suggested by Gelsser (1964). The classification rule does not have complicated distribution theory which a large variety of techniques from the sampling viewpoint have. The proposed posterior odds ratio is compared to the Gelsser's posterior odds ratio through a Monte Carlo study. The results show that the empiricla Bayes posterior odds ratio, in general, performs better than the Gelsser's. Especially, for large dimension of Z and small training sample, the performance is prominent.

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