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Principal Points and Self-Consistent Points of Symmetrical Multivariate Distributions

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  • Tarpey, T.

Abstract

The k principal points [xi]1, ..., [xi]k of a random vector X are the points that approximate the distribution of X by minimizing the expected squared distance of X to the nearest of the [xi]j. A given set of k points y1, ..., yk partition p into domains of attraction D1, ..., Dk respectively, where Dj,consists of all points x [set membership, variant] p such that [short parallel]x - yj[short parallel]

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:39-51
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    Citations

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    Cited by:

    1. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    2. Su, Yingcai, 1997. "On the Asymptotics of Quantizers in Two Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 67-85, April.
    3. Yamamoto, Wataru & Shinozaki, Nobuo, 2000. "On uniqueness of two principal points for univariate location mixtures," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 33-42, January.
    4. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
    5. Bali, Juan Lucas & Boente, Graciela, 2009. "Principal points and elliptical distributions from the multivariate setting to the functional case," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1858-1865, September.
    6. Tarpey, Thaddeus & Loperfido, Nicola, 2015. "Self-consistency and a generalized principal subspace theorem," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 27-37.
    7. Matsuura, Shun & Kurata, Hiroshi, 2011. "Principal points of a multivariate mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 213-224, February.
    8. Long-Hao Xu & Kai-Tai Fang & Ping He, 2022. "Properties and generation of representative points of the exponential distribution," Statistical Papers, Springer, vol. 63(1), pages 197-223, February.
    9. Pötzelberger Klaus & Strasser Helmut, 2001. "Clustering And Quantization By Msp-Partitions," Statistics & Risk Modeling, De Gruyter, vol. 19(4), pages 331-372, April.
    10. 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.
    11. Yang, Jun & He, Ping & Fang, Kai-Tai, 2022. "Three kinds of discrete approximations of statistical multivariate distributions and their applications," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Matsuura, Shun & Kurata, Hiroshi, 2010. "A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1863-1869, December.

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