IDEAS home Printed from https://ideas.repec.org/p/tsa/wpaper/0165mss.html
   My bibliography  Save this paper

Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure

Author

Listed:
  • Anuradha Roy

    (UTSA)

  • Roman Zmyslony
  • Miguel Fonseca
  • Ricardo Leiva

Abstract

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m??variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matrices. Complete statistics are then derived to prove that the estimators are best unbiased. Finally, strong consistency is proven. The proposed method is implemented with a real data set.

Suggested Citation

  • Anuradha Roy & Roman Zmyslony & Miguel Fonseca & Ricardo Leiva, 2015. "Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure," Working Papers 0165mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0165mss
    as

    Download full text from publisher

    File URL: http://interim.business.utsa.edu/wps/mss/0006MSS-253-2015.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sadanori Konishi & C. Khatri, 1990. "Inferences on interclass and intraclass correlations in multivariate familial data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 561-580, September.
    2. Hao, Chengcheng & Liang, Yuli & Roy, Anuradha, 2015. "Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 113-120.
    3. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    4. Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
    5. Roy, Anuradha & Leiva, Ricardo, 2008. "Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1971-1980, September.
    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. Arkadiusz Koziol & Anuradha Roy & Roman Zmyslony & Ricardo Leiva & Miguel Fonseca, 2016. "Best unbiased estimates for parameters of three-level multivariate data with doubly exchangeable covariance structure," Working Papers 0149mss, College of Business, University of Texas at San Antonio.
    2. Katarzyna Filipiak & Mateusz John & Daniel Klein, 2023. "Testing independence under a block compound symmetry covariance structure," Statistical Papers, Springer, vol. 64(2), pages 677-704, April.
    3. Ricardo Leiva & Anuradha Roy, 2016. "Multi-level multivariate normal distribution with self-similar compound symmetry covariance matrix," Working Papers 0146mss, College of Business, University of Texas at San Antonio.
    4. Roman Zmyślony & Arkadiusz Kozioł, 2021. "Ratio F test for testing simultaneous hypotheses in models with blocked compound symmetric covariance structure," Statistical Papers, Springer, vol. 62(5), pages 2109-2118, October.
    5. Roman Zmyslony & Arkadiusz Kozioł, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.
    6. Zmyślony Roman & Kozioł Arkadiusz, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.

    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. Ricardo Leiva & Anuradha Roy, 2016. "Multi-level multivariate normal distribution with self-similar compound symmetry covariance matrix," Working Papers 0146mss, College of Business, University of Texas at San Antonio.
    2. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    3. Anuradha Roy & Ricardo Leiva, 2013. "Testing the Equality of Mean Vectors for Paired Doubly Multivariate Observations," Working Papers 0180mss, College of Business, University of Texas at San Antonio.
    4. Katarzyna Filipiak & Mateusz John & Daniel Klein, 2023. "Testing independence under a block compound symmetry covariance structure," Statistical Papers, Springer, vol. 64(2), pages 677-704, April.
    5. Hao, Chengcheng & Liang, Yuli & Roy, Anuradha, 2015. "Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 113-120.
    6. Pamela C. Smith & Dana A. Forgione, 2008. "Global Outsourcing of Healthcare: A Medical Tourism Decision Model," Working Papers 0033, College of Business, University of Texas at San Antonio.
    7. Siyun Yang & Mirjam Moerbeek & Monica Taljaard & Fan Li, 2023. "Power analysis for cluster randomized trials with continuous coprimary endpoints," Biometrics, The International Biometric Society, vol. 79(2), pages 1293-1305, June.
    8. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    9. Kihoon Yoon & Daijin Ko & Carolina B. Livi & Nathan Trinklein & Mark Doderer & Stephen Kwek & Luiz O. F. Penalva, 2008. "Over-represented sequences located on UTRs are potentially involved in regulatory functions," Working Papers 0053, College of Business, University of Texas at San Antonio.
    10. Carlos A. Coelho & Anuradha Roy, 2020. "Testing the hypothesis of a doubly exchangeable covariance matrix," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 45-68, January.
    11. Liang, Yuli & Hao, Chengcheng & Dai, Deliang, 2024. "Two-sample intraclass correlation coefficient tests for matrix-valued data," Working Papers in Economics and Statistics 6/2024, Linnaeus University, School of Business and Economics, Department of Economics and Statistics.
    12. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.
    13. Bilodeau, Martin & Duchesne, Pierre, 2002. "Principal Component Analysis from the Multivariate Familial Correlation Matrix," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 457-470, August.
    14. Anuradha Roy, 2010. "Linear Models for Multivariate Repeated Measures Data," Working Papers 0017, College of Business, University of Texas at San Antonio.
    15. Tatjana Pavlenko & Anuradha Roy, 2013. "Supervised classifiers of ultra high-dimensional higher-order data with locally doubly exchangeable covariance structure," Working Papers 0185mss, College of Business, University of Texas at San Antonio.
    16. Roman Zmyslony & Arkadiusz Kozioł, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.
    17. Ivan Žežula & Daniel Klein & Anuradha Roy, 2018. "Testing of multivariate repeated measures data with block exchangeable covariance structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 360-378, June.
    18. Amitrajeet A. Batabyal & Hamid Beladi, 2015. "Optimal Transport Provision To A Tourist Destination: A Mechanism Design Approach," Working Papers 0141mss, College of Business, University of Texas at San Antonio.
    19. Seongoh Park & Johan Lim & Xinlei Wang & Sanghan Lee, 2019. "Permutation based testing on covariance separability," Computational Statistics, Springer, vol. 34(2), pages 865-883, June.
    20. Zmyślony Roman & Kozioł Arkadiusz, 2019. "Testing Hypotheses About Structure Of Parameters In Models With Block Compound Symmetric Covariance Structure," Statistics in Transition New Series, Polish Statistical Association, vol. 20(2), pages 139-153, June.

    More about this item

    Keywords

    Best unbiased estimator; blocked compound symmetric covariance structure; doubly multivariate data; coordinate free approach;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:tsa:wpaper:0165mss. 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: Wendy Frost (email available below). General contact details of provider: https://edirc.repec.org/data/cbutsus.html .

    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.