Covariance pooling and stabilization for classification

William Rayens, Tom Greene

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


It is well known that the quadratic discriminant rule (QD) is optimal for large, normal training sets in the sense of minimizing the overall misclassification rate. However, when the size of the training set is small compared to the number of variables, the performance of QD is degraded because it uses unstable sample mean vectors and covariance matrices. Friedman [8] and Greene and Rayens [9] recently proposed different methods for addressing the problem of unstable covariance matrices. This article details a critical comparison of these two methods, finding important strengths and weaknesses in both. In addition, a third discriminant rule which combines ideas from both of the aforementioned methods is developed and included in the comparisons.

Original languageEnglish
Pages (from-to)17-42
Number of pages26
JournalComputational Statistics and Data Analysis
Issue number1
StatePublished - Jan 1991


  • Cross-validation
  • Discriminant analysis
  • Empirical Bayes
  • Matrix updates

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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