The compression LS estimate of regression coefficient in multivariate linear model

Abstract

In this paper, compression LS estimate$\hat B\left( k \right)$ of the regression coefficient B is considered when the design matrix present ill-condition in multivariate linear model. The MSE (mean square error) of the estimate$\hat \beta \left( k \right) = Vec\left( {\hat B\left( k \right)} \right)$ is less than the MSE of LS estimate β^* of the regression coefficient β=Vec(B) by choosing the parameter k. Admissibility, numerical stability and relative efficiency of$\hat B\left( k \right)$ are proved. The method of determining k value for practical use is also suggested.