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

Author

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  • Roy, Anuradha
  • Zmyślony, Roman
  • Fonseca, Miguel
  • Leiva, Ricardo

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

  • Roy, Anuradha & Zmyślony, Roman & Fonseca, Miguel & Leiva, Ricardo, 2016. "Optimal estimation for doubly multivariate data in blocked compound symmetric covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 81-90.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:81-90
    DOI: 10.1016/j.jmva.2015.11.001
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    References listed on IDEAS

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    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. 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.
    5. Leiva, Ricardo, 2007. "Linear discrimination with equicorrelated training vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 384-409, February.
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    Citations

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    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. 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.
    3. 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.
    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. 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.

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    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

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