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The additive and block decompositions about the WLSEs of parametric functions for a multiple partitioned linear regression model

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  • Huang, Yunying
  • Zheng, Bing

Abstract

The necessary and sufficient conditions for the weighted least-squares estimators (WLSEs) of parametric functions K1β1+K2β2+⋯+Kmβm under a multiple partitioned linear model ℳ={y,X1β1+⋯+Xmβm,σ2Σ} to be the sum of the WLSEs of Kiβi under the m small models ℳi={y,Xiβi,σ2Σ},i=1,2,…,m, and for the WLSEs of parametric functions Kiβi under the linear model ℳ to be equal to the WLSEs of parametric function Kiβi under its small model ℳi,i=1,2,…,m are derived. Some statistical properties about the WLSEs of parametric functions are also described.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:123-135
    DOI: 10.1016/j.jmva.2014.09.009
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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.
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    6. 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.
    7. Puntanen, Simo & Styan, George P.H. & Tian, Yongge, 2005. "Three Rank Formulas Associated With The Covariance Matrices Of The Blue And The Olse In The General Linear Model," Econometric Theory, Cambridge University Press, vol. 21(3), pages 659-663, June.
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