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Some properties of projectors associated with the WLSE under a general linear model

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  • Tian, Yongge
  • Takane, Yoshio

Abstract

Projectors associated with a particular estimator in a general linear model play an important role in characterizing statistical properties of the estimator. A variety of new properties were derived on projectors associated with the weighted least-squares estimator (WLSE). These properties include maximal and minimal possible ranks, rank invariance, uniqueness, idempotency, and other equalities involving the projectors. Applications of these properties were also suggested. Proofs of the main theorems demonstrate how to use the matrix rank method for deriving various equalities involving the projectors under the general linear model.

Suggested Citation

  • Tian, Yongge & Takane, Yoshio, 2008. "Some properties of projectors associated with the WLSE under a general linear model," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1070-1082, July.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1070-1082
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    References listed on IDEAS

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    1. Yanai, Haruo, 1990. "Some generalized forms a least squares g-inverse, minimum norm g-inverse, and Moore--Penrose inverse matrices," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 251-260, December.
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    Cited by:

    1. Liu, Xin & Wang, Qing-Wen, 2013. "Equality of the BLUPs under the mixed linear model when random components and errors are correlated," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 297-309.
    2. Yongge Tian & Yoshio Takane, 2009. "On V-orthogonal projectors associated with a semi-norm," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 517-530, June.
    3. Lu, Changli & Gan, Shengjun & Tian, Yongge, 2015. "Some remarks on general linear model with new regressors," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 16-24.
    4. 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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