IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v89y2004i2p292-303.html
   My bibliography  Save this article

Maximum likelihood estimation of covariance matrices under simple tree ordering

Author

Listed:
  • Tsai, Ming-Tien

Abstract

The closed-form maximum likelihood estimators for the completely balanced multivariate one-way random effect model are obtained by Anderson et al. (Ann. Statist. 14 (1986) 405). It remains open whether there exist the closed-form maximum likelihood estimators for the more general completely balanced multivariate multi-way random effects models. In this paper, a new parameterization technique for covariance matrices is used to grasp the inside structure of likelihood function so that the maximum likelihood equations can be dramatically simplified. As such we obtain the closed-form maximum likelihood estimators of covariance matrices for Wishart density functions over the simple tree ordering set, which can then be applied to get the maximum likelihood estimators for the completely balanced multivariate multi-way random effects models without interactions.

Suggested Citation

  • Tsai, Ming-Tien, 2004. "Maximum likelihood estimation of covariance matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 292-303, May.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:2:p:292-303
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00094-0
    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. Rao, C. Radhakrishna, 1971. "Estimation of variance and covariance components--MINQUE theory," Journal of Multivariate Analysis, Elsevier, vol. 1(3), pages 257-275, September.
    2. Anderson, T. W., 1989. "The asymptotic distribution of the likelihood ratio criterion for testing rank in multivariate components of variance," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 72-79, July.
    3. Rao, C. Radhakrishna, 1971. "Minimum variance quadratic unbiased estimation of variance components," Journal of Multivariate Analysis, Elsevier, vol. 1(4), pages 445-456, December.
    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. Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.
    2. Tsai, Ming-Tien, 2007. "Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 932-944, May.
    3. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.

    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. D. Rasch & O. Mašata, 2006. "Methods of variance component estimation," Czech Journal of Animal Science, Czech Academy of Agricultural Sciences, vol. 51(6), pages 227-235.
    2. Gelein, Brigitte & Haziza, David & Causeur, David, 2014. "Preserving relationships between variables with MIVQUE based imputation for missing survey data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 197-208.
    3. H. Baltagi, Badi & Heun Song, Seuck & Cheol Jung, Byoung, 2001. "The unbalanced nested error component regression model," Journal of Econometrics, Elsevier, vol. 101(2), pages 357-381, April.
    4. Jonathan McCarthy & Egon Zakrajšek, 2000. "Microeconomic inventory adjustment: evidence from U.S. firm-level data," Staff Reports 101, Federal Reserve Bank of New York.
    5. Wu, Jixiang & Wu, Dongfeng & Jenkins, Johnie N. & McCarty, Jack Jr., 2006. "A recursive approach to detect multivariable conditional variance components and conditional random effects," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 285-300, January.
    6. Matthew Reimherr & Dan Nicolae, 2016. "Estimating Variance Components in Functional Linear Models With Applications to Genetic Heritability," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 407-422, March.
    7. S. Cheng & B. Chen, 1991. "The locally MIMSQE of nonnormal error variance in quadratically balanced models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 67-70, December.
    8. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    9. Yahia S El-Horbaty & Eman M Hanafy, 2018. "Some Estimation Methods and Their Assessment in Multilevel Models: A Review," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(3), pages 69-76, February.
    10. Fei-Yu TANG & Wang-Cheng MO & Wen-Jun XIAO, 2016. "Genetic effects of high fibre strength breeding lines in crosses with transgenic Bt cotton cultivars (Gossypium hirsutum L.)," Czech Journal of Genetics and Plant Breeding, Czech Academy of Agricultural Sciences, vol. 52(1), pages 14-21.
    11. Luis Nobre Pereira & Pedro Simoes Coelho, 2010. "Small area estimation of mean price of habitation transaction using time-series and cross-sectional area-level models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 651-666.
    12. L. Rob Verdooren, 2020. "History of the Statistical Design of Agricultural Experiments," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 457-486, December.
    13. Güven, Bilgehan, 2015. "A mixed model for complete three or higher-way layout with two random effects factors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 45-55.
    14. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January.
    15. Mathias Lindholm & Felix Wahl, 2020. "On the variance parameter estimator in general linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(2), pages 243-254, February.

    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:89:y:2004:i:2:p:292-303. 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.