IDEAS home Printed from
   My bibliography  Save this article

Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models


  • Mathew, T.
  • Niyogi, A.
  • Sinha, B. K.


Consider the independent Wishart matrices S1 W([Sigma] + [lambda][Theta],q1) and S2 W([Sigma], q2) where [Sigma] is an unknown positive definite (p.d.) matrix, [Theta] is an unknown nonnegative definite (n.n.d.) matrix, and [lambda] is a known positive scalar. For the estimation of [Theta], a class of estimators of the form [Theta](c,[epsilon]) = (c/[lambda]){S1/q1 - [epsilon](S2/q2)} (c >= 0, [epsilon] 0, [epsilon] > 0, the estimator obtained by taking the positive part of [Theta](c, [epsilon]) results in an n.n.d. estimator, say [Theta](c, [epsilon]) +, that is uniformly better than [Theta]U. Numerical results indicate that in terms of mean squared error, [Theta](c, [epsilon]) + performs much better than both [Theta]U and the restricted maximum likelihood estimator [Theta]REML of [Theta]. Similar results are also obtained for the nonnegative estimation of tr [Theta] and a'[Theta]a, where a is an arbitrary nonzero vector. For estimating [Sigma], we have derived estimators that are claimed to be uniformly better than the unbiased estimator [Sigma]U = S2/q2 under the squared error loss function and the entropy loss function. We have been able to establish the claim only in the bivariate case. Numerical results are reported showing the risk improvement of our proposed estimators of [Sigma].

Suggested Citation

  • Mathew, T. & Niyogi, A. & Sinha, B. K., 1994. "Improved Nonnegative Estimation of Variance Components in Balanced Multivariate Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 83-101, October.
  • Handle: RePEc:eee:jmvana:v:51:y:1994:i:1:p:83-101

    Download full text from publisher

    File URL:
    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 are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Oualkacha Karim & Labbe Aurelie & Ciampi Antonio & Roy Marc-Andre & Maziade Michel, 2012. "Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-27, January.
    2. Aryal, Subhash & Bhaumik, Dulal K. & Mathew, Thomas & Gibbons, Robert D., 2014. "An optimal test for variance components of multivariate mixed-effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 166-178.
    3. Kubokawa, Tatsuya & Tsai, Ming-Tien, 2006. "Estimation of covariance matrices in fixed and mixed effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2242-2261, November.
    4. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "Unified Improvements in Estimation of a Normal Covariance Matrix in High and Low Dimesions," CIRJE F-Series CIRJE-F-937, CIRJE, Faculty of Economics, University of Tokyo.
    5. Wu, Xiaoyong & Zou, Guohua & Li, Yingfu, 2009. "Uniformly minimum variance nonnegative quadratic unbiased estimation in a generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1061-1072, May.

    More about this item


    Access and download statistics


    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:51:y:1994:i:1:p:83-101. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.