Numerical treatment of restricted gauss-markov model¹

¹This work was supported in part by the Air Force of Scientific Research under the Grant AFOSR-82-0078

Abstract

The singular value decomposition (SVD) has been widely used in the ordinary linear model and other statistical problems. In this paper, we shall introduce the generalized singular value decomposition (GSVD) of any two matrices X and H having the same number of columns to moti-vate the numerical treatment of large scale restricted Gauss-Markov model (y,Xβ\Hβ = r,σ²1), a situation to reveal the relationship (or restriction) existing among the parameters of the model. Many approaches to restricted linear model are already available. Those approaches apply the generalized inverse of matrices and emphasize the the-oretical solution of the problem rather than the development of efficient and numerical stable algorithm for the computation of estimators. The possible merit of the method present here might lie in the facts that they directly lead to an efficient, numerically stable and easily programmed algorithm for

Keywords:

• restricted Gauss-Markov linear model
• gener-alized singular value decomposition
• best linear unbiased estimation

¹This work was supported in part by the Air Force of Scientific Research under the Grant AFOSR-82-0078

²Permanent Address: Institute of Mathematices, Fudan University, Shanghai, P. R. China

¹This work was supported in part by the Air Force of Scientific Research under the Grant AFOSR-82-0078

²Permanent Address: Institute of Mathematices, Fudan University, Shanghai, P. R. China

Notes

¹This work was supported in part by the Air Force of Scientific Research under the Grant AFOSR-82-0078

²Permanent Address: Institute of Mathematices, Fudan University, Shanghai, P. R. China