IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v53y1995i1p1-17.html
   My bibliography  Save this article

Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models

Author

Listed:
  • Andersson, S. A.
  • Perlman, M. D.

Abstract

The lattice conditional independence (LCI) model N() is defined to be the set of all normal distributions N(0, [Sigma]) on I such that for every pair L, M [set membership, variant] , xL and xM are conditionally independent given xL [intersection] M. Here is a ring of subsets (hence a distributive lattice) of the finite index set I such that [empty set][combining character] I [set membership, variant] , while for K [set membership, variant] , xK is the coordinate projection of x [set membership, variant] I onto K. Andersson and Perlman in the preceding paper derived the likelihood ratio (LR) statistic [lambda] for testing one LCI model against another, i.e., for testing N() vs N() based on a random sample from N(0, [Sigma]), where is a subring of . In the present paper the strict unbiasedness of the LR test is established, and related results regarding the distribution of the maximum likelihood estimator of [Sigma] under the LCI model N() are presented.

Suggested Citation

  • Andersson, S. A. & Perlman, M. D., 1995. "Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 1-17, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:1-17
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(85)71021-4
    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.

    Citations

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


    Cited by:

    1. Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    2. Jinfang Wang, 2010. "A universal algebraic approach for conditional independence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 747-773, August.
    3. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
    4. Konno, Yoshihiko, 2001. "Inadmissibility of the Maximum Likekihood Estimator of Normal Covariance Matrices with the Lattice Conditional Independence," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 33-51, October.
    5. Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.

    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:53:y:1995:i:1:p:1-17. 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: 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.