Acta mathematica scientia,Series B

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THE BLUE AND MINQUE IN GAUSS-MARKOFF MODEL WITH LINEAR#br# TRANSFORMATION OF THE OBSERVABLE VARIABLES

Zhang Baoxue; Liu Baisen   

  1. Department of Statistics, Northeast Normal University, Changchun 130024, China
  • Received:2003-12-27 Revised:1900-01-01 Online:2007-01-20 Published:2007-01-20
  • Contact: Zhang Baoxue

Abstract:

For a singular linear model A=(y,Xβ, {\si{2}} V) and its transformed model AF=(Fy,FXβ,σ2FVF), where V is nonnegative definite and X can be rank-deficient, the expressions for the
differences of the estimates for the vector of FXβ and the variance factor {\si{2}} are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor {\si{2}} are also established. In the meantime, works in Baksalary and Kala (1981) are strengthened and consequences in Puntanen and Nurhonen (1992), and Puntanen (1996) are extended.

Key words: Singular linear model, BLUE, MINQUE, linear transformation

CLC Number: 

  • 15A09
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