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The moment of inertia and the linear discriminant function

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  • Reyen, Salem S.
  • Miller, John J.

Abstract

In this note, we show that the characteristic vector of the moment of inertia matrix associated with the first or last characteristic root corresponds to the best linear discriminant function in the situation where the data is a mixture of two multivariate normal distributions with proportional covariance matrices. This result may prove useful as a part of many outlier detection methods. We also describe a small simulation study which illustrates the computational efficiency of the new method.

Suggested Citation

  • Reyen, Salem S. & Miller, John J., 2005. "The moment of inertia and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 39-46, January.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:39-46
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    References listed on IDEAS

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    1. Choulakian, V., 2001. "Robust Q-mode principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 135-150, August.
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    4. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    5. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
    6. Galpin, Jacqueline S. & Hawkins, Douglas M., 1987. "Methods of L1 estimation of a covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 305-319, September.
    7. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
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    Cited by:

    1. Salem Reyen & John Miller & Edward Wegman, 2009. "Separating a mixture of two normals with proportional covariances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 297-314, November.

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