Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

On a Balanced Classification Rule

  • Kim, Hea-Jung (Department of Statistics, Dongguk University, Seoul 100-715)
  • Published : 1995.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

We describe a constrained optimal classification rule for the case when the prior probability of an observation belonging to one of the two populations is unknown. This is done by suggesting a balanced design for the classification experiment and constructing the optimal rule under the balanced design condition. The rule si characterized by a constrained minimization of total risk of misclassification; the constraint of the rule is constructed by the process of equation between Kullback-Leibler's directed divergence measures obtained from the two population conditional densities. The efficacy of the suggested rule is examined through two-group normal classification. This indicates that, in case little is known about the relative population sizes, dramatic gains in accuracy of classification result can be achieved.

Keywords

References

  1. An Introduction to Multivariate Statistical Analysis(2nd ed.) Anderson,T.W.
  2. Annals of Statistics v.7 Expected Information as Expected Utility Bernardo,J.M.
  3. Journal of the American Statistical Association v.62 The Robustness of Hotelling's T² Dunn,O.J.;Holloway,L.N.
  4. Topics in Applied Multivariate Analysis Discriminant Analysis Fatti,L.P.;Hawkins,D.M.;Raath,L.R.
  5. Journal of the American Statistical Association v.84 Regularized Discriminant Analysis Friedman,J.H.
  6. Biometrics v.35 The Effect of Unequal Variance-Covariance Matrices on Fisher's Linear Discriminant Function Gilbert,E.S.
  7. Journal of the American Statistical Association v.67 Sample-Based Classification Procedures Derived from Density Estimators Glick,N.
  8. Discrete Discriminant Analysis Goldstein,M.;Dillon,W.R.
  9. Applied Multivariate Statistical Analysis(3rd ed.) Johnson,R.A.;Wichern,D.W.
  10. Entropy Optimization Principles with Applications Kapur,J.N.;Kesavan,H.K.
  11. The Advanced Theory of Statistics v.2 Kendall,M.C.;Stuart,A.
  12. Annals of Mathematical Statistics v.22 On Information and Sufficiency Kullback,S.;Leibler,R.A.
  13. Introduction to Probability and Statistics v.1 Lindley,D.V.
  14. Journal of the American Statistical Association v.69 Discriminant Functions when Covariance Matrices are Unequal Marks,S.;Dunn,O.J.
  15. Biometrika v.36 The Noncentral χ² and F-distributions and their Approximations Patnaik,P.B.
  16. Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference Press,S.J.
  17. Annals of Mathematical Statistics v.15 On a Statistical Problem Arising in the Classification of an Individual into One of Two Groups Wald,A.