IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v108y2012icp53-66.html
   My bibliography  Save this article

Estimation of parameters in the growth curve model via an outer product least squares approach for covariance

Author

Listed:
  • Hu, Jianhua
  • Liu, Fuxiang
  • Ahmed, S. Ejaz

Abstract

In this paper, we propose a framework of outer product least squares for covariance (COPLS) to directly estimate covariance in the growth curve model based on an analogy, between the outer product of a data vector and covariance of a random vector, and the ordinary least squares technique. The COPLS estimator of covariance has an explicit expression and is shown to have the following properties: (1) following a linear transformation of two independent Wishart distribution for a normal error matrix; (2) having asymptotic normality for a nonnormal error matrix; and (3) having unbiasedness and invariance under a linear transformation group. And, a corresponding two-stage generalized least squares (GLS) estimator for the regression coefficient matrix in the model is obtained and its asymptotic normality is investigated. Simulation studies confirm that the COPLS estimator and the two-stage GLS estimator of the regression coefficient matrix are satisfying competitors with some evident merits to the existing maximum likelihood estimator in finite samples.

Suggested Citation

  • Hu, Jianhua & Liu, Fuxiang & Ahmed, S. Ejaz, 2012. "Estimation of parameters in the growth curve model via an outer product least squares approach for covariance," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 53-66.
    • Handle: RePEc:eee:jmvana:v:108:y:2012:i:c:p:53-66
    DOI: 10.1016/j.jmva.2012.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000413
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.02.007?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
    ---><---

    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. Hu, Jianhua, 2008. "Wishartness and independence of matrix quadratic forms in a normal random matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 555-571, March.
    2. von Rosen, Dietrich, 1989. "Maximum likelihood estimators in multivariate linear normal models," Journal of Multivariate Analysis, Elsevier, vol. 31(2), pages 187-200, November.
    3. Ohlson, Martin & von Rosen, Dietrich, 2010. "Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1284-1295, May.
    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. Veronika Kopčová & Ivan Žežula, 2020. "On intraclass structure estimation in the growth curve model," Statistical Papers, Springer, vol. 61(3), pages 1085-1106, June.
    2. Hu, Jianhua & Xin, Xin & You, Jinhong, 2014. "Model determination and estimation for the growth curve model via group SCAD penalty," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 199-213.

    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. Pan, Jianxin, 2004. "Discordant outlier detection in the growth curve model with Rao's simple covariance structure," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 135-142, August.
    2. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Pan, Jian-Xin & Fang, Kai-Tai & von Rosen, Dietrich, 1998. "On the posterior distribution of the covariance matrix of the growth curve model," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 33-39, May.
    4. Saulo, Helton & Vila, Roberto & Cordeiro, Shayane S. & Leiva, Víctor, 2023. "Bivariate symmetric Heckman models and their characterization," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    5. Fang, Kai-Tai & Wang, Song-Gui & von Rosen, Dietrich, 2006. "Restricted expected multivariate least squares," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 619-632, March.
    6. Rastislav Rusnačko & Ivan Žežula, 2016. "Connection between uniform and serial correlation structure in the growth curve model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 149-164, February.
    7. Yang, Guo-Qing & Wu, Qi-Guang, 2004. "Existence conditions for the uniformly minimum risk unbiased estimators in a class of linear models," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 76-88, January.
    8. Wu, Xiaoyong & Zou, Guohua & Chen, Jianwei, 2006. "Unbiased invariant minimum norm estimation in generalized growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1718-1741, September.
    9. Hamid, Jemila S. & Beyene, Joseph & von Rosen, Dietrich, 2011. "A novel trace test for the mean parameters in a multivariate growth curve model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 238-251, February.
    10. Bai, Peng & Shi, Lei, 2007. "Exact distributions of MLEs of regression coefficients in GMANOVA-MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1840-1852, October.
    11. Phil D. Young & Joshua D. Patrick & Dean M. Young, 2023. "A Brief Derivation of Necessary and Sufficient Conditions for a Family of Matrix Quadratic Forms to Have Mutually Independent Non-Central Wishart Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 478-484, February.
    12. Jian-Xin Pan & Kai-Tai Fang, 1996. "Influential observation in the growth curve model with unstructured covariance matrix," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 71-87, June.
    13. Hamid Jemila S & Beyene Joseph, 2009. "A Multivariate Growth Curve Model for Ranking Genes in Replicated Time Course Microarray Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-28, July.
    14. Li, Ying & Udén, Peter & von Rosen, Dietrich, 2015. "A two-step estimation method for grouped data with connections to the extended growth curve model and partial least squares regression," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 347-359.
    15. Veronika Kopčová & Ivan Žežula, 2020. "On intraclass structure estimation in the growth curve model," Statistical Papers, Springer, vol. 61(3), pages 1085-1106, June.
    16. Jana, Sayantee & Balakrishnan, Narayanaswamy & Hamid, Jemila S., 2018. "Estimation of the parameters of the extended growth curve model under multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 111-128.
    17. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2021. "On properties of Toeplitz-type covariance matrices in models with nested random effects," Statistical Papers, Springer, vol. 62(6), pages 2509-2528, December.
    18. Pierpaolo Angelini & Fabrizio Maturo, 2022. "The consumer’s demand functions defined to study contingent consumption plans," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(3), pages 1159-1175, June.
    19. Hu, Jianhua & Xin, Xin & You, Jinhong, 2014. "Model determination and estimation for the growth curve model via group SCAD penalty," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 199-213.
    20. Angelini, Pierpaolo & Maturo, Fabrizio, 2022. "The price of risk based on multilinear measures," International Review of Economics & Finance, Elsevier, vol. 81(C), pages 39-57.

    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:108:y:2012:i:c:p:53-66. 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.