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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.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 76 (2006)
Issue (Month): 12 (July)
Pages: 1265-1272

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Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1265-1272

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Keywords: General linear model Equality Proportionality OLSE WLSE BLUE Projectors Rank formulas for partitioned matrices;

References

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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. 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.
  2. Yuqin Sun & Rong Ke & Yongge Tian, 2014. "Some overall properties of seemingly unrelated regression models," AStA Advances in Statistical Analysis, Springer, vol. 98(2), pages 103-120, April.
  3. 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.
  4. 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, vol. 63(4), pages 851-871, August.
  5. 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, Springer, vol. 76(5), pages 707-722, July.

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