Generalized inverse estimator and comparison with least squares estimator

Abstract

Trenkler [13] described an iteration estimator. This estimator is defined as follows: for $0 < \gamma < 1/\lambda_i$ max $\hat{\beta}_{m,\gamma}=\gamma\sum\limits_{i=0}^m(1- \gamma X' X)^iX'y$ where $\lambda_i$ are eigenvalues of X'X. In this paper a new estimator (generalized inverse estimator) is introduced based on the results of Tewarson [11]. A sufficient condition for the difference of mean square error matrices of least squares estimator and generalized inverse estimator to be positive definite (p.d.) is derived.Trenkler [13] described an iteration estimator. This estimator is defined as follows: for $0 < \gamma < 1/\lambda_i$ max $\hat{\beta}_{m,\gamma}=\gamma\sum\limits_{i=0}^m(1- \gamma X' X)^iX'y$ where $\lambda_i$ are eigenvalues of X'X. In this paper a new estimator (generalized inverse estimator) is introduced based on the results of Tewarson [11]. A sufficient condition for the difference of mean square error matrices of least squares estimator and generalized inverse estimator to be positive definite (p.d.) is derived