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A principal subspace theorem for 2-principal points of general location mixtures of spherically symmetric distributions

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  • Matsuura, Shun
  • Kurata, Hiroshi

Abstract

In this paper, we study 2-principal points of general location mixtures, including finite and infinite mixtures, of spherically symmetric distributions. A theorem is established that clarifies a linear subspace in which any set of 2-principal points exists.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1863-1869
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    References listed on IDEAS

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    1. Thaddeus Tarpey, 1997. "Estimating principal points of univariate distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(5), pages 499-512.
    2. Tarpey, Thaddeus, 1994. "Two principal points of symmetric, strongly unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 253-257, July.
    3. 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.
    4. Li, Luning & Flury, Bernard, 1995. "Uniqueness of principal points for univariate distributions," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 323-327, December.
    5. Tarpey, Thaddeus, 2007. "Linear Transformations and the k-Means Clustering Algorithm: Applications to Clustering Curves," The American Statistician, American Statistical Association, vol. 61, pages 34-40, February.
    6. 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.
    7. 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.
    8. Thaddeus Tarpey, 2007. "A parametric k-means algorithm," Computational Statistics, Springer, vol. 22(1), pages 71-89, April.
    9. Tarpey T. & Petkova E. & Ogden R.T., 2003. "Profiling Placebo Responders by Self-Consistent Partitioning of Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 850-858, January.
    10. 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.
    11. Su, Yingcai, 1997. "On the Asymptotics of Quantizers in Two Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 67-85, April.
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    Cited by:

    1. Shun Matsuura & Thaddeus Tarpey, 2020. "Optimal principal points estimators of multivariate distributions of location-scale and location-scale-rotation families," Statistical Papers, Springer, vol. 61(4), pages 1629-1643, August.
    2. Loperfido, Nicola, 2014. "A note on the fourth cumulant of a finite mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 386-394.
    3. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
    4. Tarpey, Thaddeus & Loperfido, Nicola, 2015. "Self-consistency and a generalized principal subspace theorem," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 27-37.
    5. Santanu Chakraborty & Mrinal Kanti Roychowdhury & Josef Sifuentes, 2021. "High Precision Numerical Computation of Principal Points for Univariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 558-584, November.
    6. 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.
    7. 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).

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