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

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 Xb in the general linear (Gauss-Markov) model M ¼ fy; Xb; s 2 Rg are investigated through the matrix rank method. r

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References (11)

  1. Baksalary, J.K., Puntanen, S., 1989. Weighted-least squares estimation in the general Gauss-Markov model. In: Dodge, Y. (Ed.), Statistical Data Analysis and Inference. Elsevier, New York, pp. 355-368.
  2. GroX, G., Trenkler, T., Werner, H.J., 2001. The equality of linear transformations of the ordinary least squares estimator and the best linear unbiased estimator. Sankhya ¯Ser. A 63, 118-127.
  3. Marsaglia, G., Styan, G.P.H., 1974. Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra 2, 269-292.
  4. Mathew, T., 1983. Linear estimation with an incorrect dispersion matrix in linear models with a common linear part. J. Amer. Statist. Assoc. 78, 468-471.
  5. Mitra, S.K., Moore, B.J., 1973. Gauss-Markov estimation with an incorrect dispersion matrix. Sankhya ¯Ser. A 35, 139-152.
  6. Mitra, S.K., Rao, C.R., 1974. Projections under seminorms and generalized Moore-Penrose inverses. Linear Algebra Appl. 9, 155-167.
  7. Puntanen, S., Styan, G.P.H., 1989. The equality of the ordinary least squares estimator and the best linear unbiased estimator. With comments by O. Kempthorne, S.R. Searle, and a reply by the authors. Amer. Statist. 43, 153-164.
  8. Rao, C.R., 1971. Unified theory of linear estimation. Sankhya ¯Ser. A 33, 371-394.
  9. Tian, Y., 2002. The maximal and minimal ranks of some expressions of generalized inverses of matrices. Southeast Asian Bull. Math. 25, 745-755.
  10. Tian, Y., Cheng, S., 2003. The maximal and minimal ranks of A À BXC with applications. New York J. Math. 9, 345-362.
  11. Young, D.M., Odell, P.L., Hahn, W., 2000. Nonnegative-definite covariance structures for which the blu, wls, and ls estimators are equal. Statist. Probab. Lett. 49, 271-276.