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On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models

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  • Changli Lu
  • Yuqin Sun
  • Yongge Tian

Abstract

We study relations between the weighted least-squares estimators (WLSEs) of given parametric functions $$\mathbf{K}_1\varvec{\beta }_1 + \mathbf{K}_2\varvec{\beta }_2$$ under a general partitioned linear model $${\fancyscript{M}}=\{ \mathbf{y}, \, \mathbf{X}_1\varvec{\beta }_1 + \mathbf{X}_2\varvec{\beta }_2, \, \sigma ^2\varvec{\Sigma }\}$$ and the WLSEs of $$\mathbf{K}_1\varvec{\beta }_1$$ and $$\mathbf{K}_2\varvec{\beta }_2$$ under the two small models $$\{ \mathbf{y}, \, \mathbf{X}_1\varvec{\beta }_1, \, \sigma ^2\varvec{\Sigma }\}$$ and $$\{ \mathbf{y}, \, \mathbf{X}_2\varvec{\beta }_2, \,\sigma ^2\varvec{\Sigma }\}$$ . Some consequences on additive decomposition of the best unbiased linear estimator (BLUE) of $$\mathbf{K}_1\varvec{\beta }_1 + \mathbf{K}_2\varvec{\beta }_2$$ under $${\fancyscript{M}}$$ are also given. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Changli Lu & Yuqin Sun & Yongge Tian, 2013. "On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 707-722, July.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:5:p:707-722
    DOI: 10.1007/s00184-012-0412-x
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    References listed on IDEAS

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    1. Yongge Tian, 2007. "Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model," International Statistical Review, International Statistical Institute, vol. 75(2), pages 224-248, August.
    2. Tian, Yongge, 2009. "On an additive decomposition of the BLUE in a multiple-partitioned linear model," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 767-776, April.
    3. Yongge Tian, 2010. "On equalities of estimations of parametric functions under a general linear model and its restricted models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 313-330, November.
    4. Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
    5. Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
    6. Gourieroux, Christian & Monfort, Alain, 1980. "Sufficient Linear Structures: Econometric Applications," Econometrica, Econometric Society, vol. 48(5), pages 1083-1097, July.
    7. Yongge Tian, 2010. "Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 929-941, October.
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    Cited by:

    1. Huang, Yunying & Zheng, Bing, 2015. "The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 123-135.

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