A BLUE decomposition in the general linear regression model


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Werner H., Yapar C.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.237, pp.395-404, 1996 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 237
  • Publication Date: 1996
  • Doi Number: 10.1016/0024-3795(95)00542-0
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.395-404

Abstract

In this note we consider the general linear regression model (y, X beta,V\R(2) beta(2) = r) where the block partitioned regressor matrix X = (X(1) X(2)) may be deficient in column rank, the dispersion matrix V is possibly singular, beta(t) = (beta(1)(t) beta(2)(t))-being partitioned according to X-is the vector of unknown regression coefficients, and Pt is possibly subject to consistent linear constraints R(2) beta(2) = r. Of much interest to us is the traditional BLUE (best linear unbiased estimator) of X beta. We show how this traditional BLUE can obtained from the traditional BLUE of X(1) beta(1) in the related model (y, X(1) beta(1), V). Some properties of the dispersion matrix of the traditional BLUE of X beta are also given.