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On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model

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  • Tian, Yongge
  • Wiens, Douglas P.

Abstract

Equality and proportionality of the ordinary least-squares estimator (OLSE), the weighted least-squares estimator (WLSE), and the best linear unbiased estimator (BLUE) for X[beta] in the general linear (Gauss-Markov) model are investigated through the matrix rank method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1265-1272
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    References listed on IDEAS

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    1. Young, Dean M. & Odell, Patrick L. & Hahn, William, 2000. "Nonnegative-definite covariance structures for which the blu, wls, and ls estimators are equal," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 271-276, September.
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    Cited by:

    1. Chong Ji & Wenhui Zhao & Hui Wang & Puyu Yuan, 2022. "Online Platform Customer Shopping Repurchase Behavior Analysis," Sustainability, MDPI, vol. 14(14), pages 1-14, July.
    2. Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
    3. Yuqin Sun & Rong Ke & Yongge Tian, 2014. "Some overall properties of seemingly unrelated regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 103-120, April.
    4. 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.
    5. 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.
    6. Zhiping Xiong & Yingying Qin, 2014. "Extremal Ranks of Some Nonlinear Matrix Expressions with Applications," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 595-613, November.
    7. Alessandra Luati & Tommaso Proietti, 2011. "On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 851-871, August.
    8. Ren, Xingwei, 2014. "On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 1-10.

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