IDEAS home Printed from https://ideas.repec.org/a/bla/anzsta/v45y2003i2p229-249.html
   My bibliography  Save this article

Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two‐Dimensional Marginals

Author

Listed:
  • Satoshi Aoki
  • Akimichi Takemura

Abstract

This paper considers a connected Markov chain for sampling 3 × 3 ×K contingency tables having fixed two‐dimensional marginal totals. Such sampling arises in performing various tests of the hypothesis of no three‐factor interactions. A Markov chain algorithm is a valuable tool for evaluating P‐values, especially for sparse datasets where large‐sample theory does not work well. To construct a connected Markov chain over high‐dimensional contingency tables with fixed marginals, algebraic algorithms have been proposed. These algorithms involve computations in polynomial rings using Gröbner bases. However, algorithms based on Gröbner bases do not incorporate symmetry among variables and are very time‐consuming when the contingency tables are large. We construct a minimal basis for a connected Markov chain over 3 × 3 ×K contingency tables. The minimal basis is unique. Some numerical examples illustrate the practicality of our algorithms.

Suggested Citation

  • Satoshi Aoki & Akimichi Takemura, 2003. "Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two‐Dimensional Marginals," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 229-249, June.
    • Handle: RePEc:bla:anzsta:v:45:y:2003:i:2:p:229-249
    DOI: 10.1111/1467-842X.00278
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-842X.00278
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-842X.00278?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Elizabeth Gross & Sonja Petrović & Despina Stasi, 2017. "Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 673-704, June.
    2. Akimichi Takemura & Hisayuki Hara, 2007. "Conditions for swappability of records in a microdata set when some marginals are fixed," Computational Statistics, Springer, vol. 22(1), pages 173-185, April.

    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:bla:anzsta:v:45:y:2003:i:2:p:229-249. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1369-1473 .

    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.