IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v61y1997i1p67-85.html
   My bibliography  Save this article

On the Asymptotics of Quantizers in Two Dimensions

Author

Listed:
  • Su, Yingcai

Abstract

When the mean square distortion measure is used, asymptotically optimal quantizers of uniform bivariate random vectors correspond to the centers of regular hexagons (Newman, 1982), and if the random vector is non-uniform, asymptotically optimal quantizers are the centers of piecewise regular hexagons where the sizes of the hexagons are determined by a properly chosen density function (Su and Cambanis, 1996). This paper considers bivariate random vectors with finite[gamma]th ([gamma]>0) moment. If the[gamma]th mean distortion measure is used, a complete characterization of the asymptotically optimal quantizers is given. Furthermore, it is shown that the procedure introduced by Su and Cambanis (1996) is also asymptotically optimal for every[gamma]>0. Examples with a normal distribution and a Pearson type VII distribution are considered.

Suggested Citation

  • Su, Yingcai, 1997. "On the Asymptotics of Quantizers in Two Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 67-85, April.
    • Handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:67-85
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91663-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Su, Yingcai, 1997. "Estimation of random fields by piecewise constant estimators," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 145-163, November.
    2. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
    3. Matsuura, Shun & Kurata, Hiroshi, 2011. "Principal points of a multivariate mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 213-224, February.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Shun Matsuura & Hiroshi Kurata, 2014. "Principal points for an allometric extension model," Statistical Papers, Springer, vol. 55(3), pages 853-870, August.
    5. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    6. Matsuura, Shun & Kurata, Hiroshi, 2011. "Principal points of a multivariate mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 213-224, February.
    7. 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.
    8. Tarpey, Thaddeus & Loperfido, Nicola, 2015. "Self-consistency and a generalized principal subspace theorem," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 27-37.
    9. 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).
    10. Pötzelberger Klaus & Strasser Helmut, 2001. "Clustering And Quantization By Msp-Partitions," Statistics & Risk Modeling, De Gruyter, vol. 19(4), pages 331-372, April.
    11. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:67-85. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.