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Estimation of variance and covariance components--MINQUE theory

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  • Rao, C. Radhakrishna

Abstract

The paper consists of two parts. The first part deals with solutions to some optimization problems. The general problem is one of minimssing Tr AVA'U, where V and U are positive definite matrices when the elements of the matrix are subject to linear restrictions of the type AX = O or X'AX = O and trace AVi = pi, i = 1,..., k, or U1'AU1 + ... + Uk'AUk = M. These results are used in determining Minimum Norm Quadratic Unbiased Estimators (MINQUE) of variance and covariance components in linear models. The present paper is a generalization of an earlier attempt by the author to obtain estimators of heteroscedastic variances in a regression model. The method is quite general, applicable to all experimental situations, and the computations are simple.

Suggested Citation

  • Rao, C. Radhakrishna, 1971. "Estimation of variance and covariance components--MINQUE theory," Journal of Multivariate Analysis, Elsevier, vol. 1(3), pages 257-275, September.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:3:p:257-275
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January.
    12. 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.
    13. 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.

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