Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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On an Information Theoretic Diagnostic Measure for Detecting Influential Observations in LDA

  • Published : 1996.06.01
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Abstract

This paper suggests a new diagnostic measure for detecting influential observations in two group linear discriminant analysis(LDA). It is developed from an information theoretic point of view using the minimum discrimination information(MDI) methodology. MDI estimator of symmetric divergence by Kullback(l967) is taken as a measure of the power of discrimination in LDA. It is shown that the effect of an observation over the power of discrimination is fully explained by the diagnostic measure. Asymptotic distribution of the proposed measure is derived as a function of independent chi-squared and standard normal variables. By means of the distributions, a couple of methods are suggested for detecting the influential observations in LDA. Performance of the suggested methods are examined through a simulation study.

Keywords

References

  1. Applied Statistics v.27 The influence function as an aid in outlier detection in discriminant analysis Campbell, N. A.
  2. Technometrics v.19 Detection of influential observation in linear regression Cook, D. R.
  3. Biometrika v.78 The influence of observations on misclassification probability estimates in linear discriminant analysis Critchley,F.;Vitiello, C.
  4. Statistics and Probability Letters v.13 Some diagnostic measures in discriminant analysis Fung, W. K.
  5. Journal of the American Statistical Association v.90 Diagnostics in linear discriminant analysis Fung, W. K.
  6. Journal of Business and Economic Statistics v.5 The detection of influential observations for allocation, separation, and the determination of probabilities in a Bayesian framework Johnson, W.
  7. Entropy Optimization Principles with Applications Kapur, J. N.;Kesavan, H. K.
  8. Communications in Statistics: Theory and Methods v.24 no.3 On a balanced quadratic classification Kim, H. J.
  9. Journal of Multivariate Analysis On a constrained optimal rule for classification with unknown prior individual group membership Kim, H. J.
  10. Information Theory and Statistics Kullback, S.
  11. Metron, XLI-X, 1-2 v.30 Influence functions for certain parameters in discriminant analysis Radhakrishnan, R.
  12. Journal of the American Statistical Association v.85 Unmasking multivariate outliers and leverage points (with discussion) Rousseeuw, P. J.;van Zomeren