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Estimation of the probabilities of misclassification for a linear discriminant function in the univariate normal case

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Summary

The probability of misclassification inherent in the use of a linear discriminant function is not necessarily known to the experimenter using such a function. Various estimators calculated from the sample used to generate the sample discriminant function have been proposed. The purpose of this paper is to evaluate and to compare several of these estimators by using unconditional mean square error as the criterion. Discussion is restricted to the case where each of the distributions is univariate normal with common variance.

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References

  1. Anderson, T. W. (1951). Classification by multivariate analysis,Psychometrika,16, 31–50.

    Article  MathSciNet  Google Scholar 

  2. Geisser, S. (1967). Estimation associated with linear discriminants,Ann. Math. Statist.,38, 807–817.

    MATH  MathSciNet  Google Scholar 

  3. Hill, M. (1966). Allocation rules and their error rates,J. Roy. Statist. Soc. Ser. B,28, 1–32.

    MathSciNet  Google Scholar 

  4. John, S. (1961). Errors in discrimination,Ann. Math. Statist. 32, 1125–1144.

    MATH  MathSciNet  Google Scholar 

  5. Lachenbruch, P. A. and Mickey, M. R. (1968). Estimation of error rates in discriminant analysis,Technometrics,10, 1–11.

    Article  MathSciNet  Google Scholar 

  6. Okamoto, M. (1963). An asymptotic expansion for the distribution of the linear discriminant function,Ann. Math. Statist.,34, 1286–1301.

    MATH  MathSciNet  Google Scholar 

  7. Sedransk, N. (1969). Contributions to discriminant analysis,Ph.D. thesis, Iowa State University.

  8. Smith, C. A. B. (1947). Some examples of discrimination,Ann. Eugenics,13, 272–282.

    MathSciNet  Google Scholar 

  9. Sorum, M. J. (1968). Estimating the probability of misclassification,Ph.D. Dissertation, Univ. of Minnesota.

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Authors and Affiliations

  1. Iowa State University, Iowa, USA

    N. Sedransk & Masashi Okamoto

  2. University of Wisconsin, Wisconsin, USA

    N. Sedransk & Masashi Okamoto

  3. Osaka University, Osaka, Japan

    N. Sedransk & Masashi Okamoto

Authors
  1. N. Sedransk
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  2. Masashi Okamoto
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Additional information

This paper is partially based on the Ph.D. thesis of N. Sedransk [7] at Iowa State University.

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Sedransk, N., Okamoto, M. Estimation of the probabilities of misclassification for a linear discriminant function in the univariate normal case. Ann Inst Stat Math 23, 419–435 (1971). https://doi.org/10.1007/BF02479241

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  • DOI: https://doi.org/10.1007/BF02479241

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