On Relationship Between the AIC and the Overall Error Rates for Selection of Variables in a Discriminant Analysis

  • Yasunori Fujikoshi
Part of the Theory and Decision Library book series (TDLB, volume 8)


This paper deals with the problem of selecting the “best” subset of variables in a discriminant analysis with the aim of allocating future observations, in the context of two multivariate normal populations with the same covariance matrix. We consider the methods based on the following three criteria: (i) the AIC for the “no additional information” model, (ii) the overall error rate criterion based on the linear classification statistic and (iii) the overall error rate criterion based on the ML classification statistic. It is shown that there is a close relationship between the AIC and the overall error rate criteria.


Error Rate Discriminant Analysis Asymptotic Expansion Asymptotic Distribution Classification Statistic 
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  1. Akaike, H. (1973). ‘Information theory and an extension of the maximum likelihood principle’. In: 2nd International Symposium on Information Theory (B. N. Petrov and F. Czáki, eds.), pp.267–281, Akademiai Kiadó, Budapest.Google Scholar
  2. Fujikoshi, Y. (1983). ‘A criterion for variable selection in multiple discriminant analysis’. Hiroshima Math. J. 13, 203–214.MathSciNetzbMATHGoogle Scholar
  3. Fujikoshi, Y. (1985 a). ‘Selection of variables in two-group discriminant analysis by error rate and Akaike’s information criteria’. J. Multiv. Anal. 17, 27–37.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Fujikoshi, Y. (1985 b). ‘Selection of variables in discriminant analysis and canonical correlation analysis. In: Multivariate Analysis — VI (P. R. Krishnaiah, ed.), pp.219–236, North-Holland.Google Scholar
  5. McLachlan, G. J. (1973). ‘An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis’. Austral. J. Statist. 15, 210–214.MathSciNetzbMATHCrossRefGoogle Scholar
  6. McLachlan, G. J. (1980). ‘On the relationship between the F test and the overall error rate for variable selection in two-group discriminant analysis’. Biometrics 36, 501–510.zbMATHCrossRefGoogle Scholar
  7. McKay, R. J. and Campbell, N. A. (1982). ‘Variable selection techniques in discriminant analysis I. Description’. British J. Math. Statist. Psychology 35, 1–29.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Mckay, R. J. and Campbell, N. A. (1982). ‘Variable selection techniques in discriminant analysis II. Allocation’. British J. Math. Statist. Psychology 35, 30–41.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Memon, A. Z. and Okamoto, M. (1971). ‘Asymptotic expansion of the distribution of the Z statistic in discriminant analysis’. J. Multiv. Anal. 1, 294–307.MathSciNetCrossRefGoogle Scholar
  10. Okamoto, M. (1963). ‘An asymptotic expansion for the distribution of the linear discriminant function’. Ann. Math. Statist. 34, 1286–1301.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Rao, C. R. (1970). ‘Inference on discriminant function coefficients’. In: Essays in Prob, and Statist. (R. C. Bose, ed.), pp.587–602. Univ. of North Carolina Press, Chapel Hill.Google Scholar
  12. Shibata, R. (1976). ‘Selection of the order of an auto-regressive model by Akaike’s information criterion’. Biometrika 63, 117–126.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Spitzer, F. (1956). A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82, 323–339.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1987

Authors and Affiliations

  • Yasunori Fujikoshi
    • 1
  1. 1.Department of Mathematics Faculty of ScienceHiroshima UniversityHiroshimaJapan

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