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Distribution of discriminant function in circular models

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Summary

Assuming that the covariance matrices are circular, we make an appropriate transformation which reduces the circular matrices to canonical forms. The discriminant function is given when the populations are multivariate normal with different circular matrices and its distribution is derived. An asymptotic expansion for the distribution is obtained when all the parameters are unknown.

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References

  1. Han, C. P. (1969). Distribution of discriminant function when covariance matrices are proportional,Ann. Math. Statist.,40, 979–985.

    MATH  MathSciNet  Google Scholar 

  2. Hartley, H. O. (1938). Studentization and large-sample theory,J. Roy. Statist. Soc., Suppl.,5, 80–88.

    Article  MATH  Google Scholar 

  3. Ito, Koichi (1956). Asymptotic formulae for the distribution of Hotelling's generalizedT 0 2 statistic I,Ann. Math. Statist.,27, 1091–1105; (1960), II,Ann. Math. Statist.,31, 1148–1153.

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  5. Patnaik, D. B. (1949). The non-central χ3 andF-distributions and their applications,Biometrika,36, 202–232.

    Article  MATH  MathSciNet  Google Scholar 

  6. Siotani, M. (1957). On the distribution of the Hotelling'sT 2-statistics,Ann. Inst. Statist. Math.,8, 1–14.

    Article  MathSciNet  Google Scholar 

  7. Wallace, D. L. (1958). Asymptotic approximations to distributions,Ann. Math. Statist.,29, 635–654.

    MATH  MathSciNet  Google Scholar 

  8. Welch, B. L. (1947). The generalization of ‘Student's’ problem when several different population variances are involved,Biometrika,34, 28–35.

    Article  MATH  MathSciNet  Google Scholar 

  9. Whittle, P. (1951).Hypothesis Testing in Time Series Analysis, Uppsala, Sweden: Almquist and Wiksells.

    MATH  Google Scholar 

  10. Wise, J. (1955). The autocorrelation function and the spectral density function,Biometrika,42, 151–159.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Statistical Laboratory, Iowa State University, Iowa, USA

    Chien-Pai Han

Authors
  1. Chien-Pai Han
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Additional information

This research is partially supported by National Institutes of Health Grant No. GM 00034-12.

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Han, CP. Distribution of discriminant function in circular models. Ann Inst Stat Math 22, 117–125 (1970). https://doi.org/10.1007/BF02506327

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  • DOI: https://doi.org/10.1007/BF02506327

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