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On linear classification procedures between two categories with known mean vectors and covariance matrices

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Summary

This paper is concerned with probabilities (error probabilities), caused by misclassification, of linear classification procedures (linear procedures) between two categories, whose mean vectors and covariance matrices are assumed to be known, while the distribution of each category may well be continuous or discrete. The tightest upper bounds on the largest of two kinds of error probability of each linear procedure and on the expected error probability for any apriori probabilities are obtained. Moreover in some cases of interest, theoptimal linear procedure (in the sense of attaining the infimum out of all the upper bounds) is given.

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References

  1. Anderson, T. W. (1958).An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, Inc.

  2. Anderson, T. W. and Bahadur, R. R. (1962). Classification into two multivariate normal distributions with different covariance matrices,Ann. Math. Statist.,33, 420–431.

    MathSciNet  MATH  Google Scholar 

  3. Chernoff, H. (1971). A bound on the classification error for discriminating between populations with specified means and variances,Studi Prob. Statist. Ric. Operat. 203–211.

  4. Cramér, H. (1946).Mathematical Methods of Statistics, Princeton Univ. Press.

  5. Isii, K. (1964). Inequalities of the types of Chebyshev and Cramér-Rao and mathematical programming,Ann. Inst. Statist. Math.,16, 277–293.

    MathSciNet  Google Scholar 

  6. Isii, K. and Taga, Y. (1975). Mathematical programming approach to a minimax theorem of statistical discrimination applicable to pattern recognition,Optimization Techniques IFIP Technical Conference, Novosibirsk July 1974, Springer-Verlag, 348–352.

  7. Lachenbruch, P. A., Sneeringer, C. and Revo, L. T. (1972). Robustness of the linear and quadratic discriminant function to certain types of non-normality,Commun. Statist.,1, 39–56.

    Google Scholar 

  8. Yau, S. S. and Lin, T. T. (1968). On the upper bound of the probability of error of a linear pattern classifier for probabilistic pattern classes,Proc. IEEE.,56, 321–322.

    Article  Google Scholar 

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Authors and Affiliations

  1. Shizuoka University, Shizuoka, Japan

    Akihiro Nishi

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  1. Akihiro Nishi
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Nishi, A. On linear classification procedures between two categories with known mean vectors and covariance matrices. Ann Inst Stat Math 29, 433–444 (1977). https://doi.org/10.1007/BF02532804

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  • DOI: https://doi.org/10.1007/BF02532804

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