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Parallel Principal Axes

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  • Tarpey, Thaddeus

Abstract

Parallel principal axes are introduced and used to investigate the structure of multivariate distributions. In the class of elliptical distributions, it is shown that self-consistency of parallel principal axes characterizes normality. Parallel principal axes are used to illustrate the equivalent event fallacy in the context of self-consistency. Finally, the idea of piecewise principal component axes is introduced and related to an allometric extension model.

Suggested Citation

  • Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    • Handle: RePEc:eee:jmvana:v:75:y:2000:i:2:p:295-313
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    References listed on IDEAS

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    1. Tarpey, T., 1995. "Principal Points and Self-Consistent Points of Symmetrical Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 39-51, April.
    2. Rao, M. M., 1988. "Paradoxes in conditional probability," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 434-446, November.
    3. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    4. Neuenschwander, Beat E. & Flury, Bernard D., 1997. "A note on Silvey's (1959) Theorem," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 307-317, December.
    5. Bernard D. Flury, 1993. "Estimation of Principal Points," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 139-151, March.
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    Cited by:

    1. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
    2. Kurata, Hiroshi & Hoshino, Takahiro & Fujikoshi, Yasunori, 2008. "Allometric extension model for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1985-1998, October.

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