Dergiler / Turkish Journal of Mathematics / 1998 / Cilt: 22 - Sayı: 1
Generalized Inverse Estimator and comparison with Least Squares Estimator
- Sayfa
- 77–84
- DOI
- —
Özet
Trenkler [13] described an iteration estimator. This estimator is defined as follows: for 0 < g < 1/li \max \[ \hat{b}m, g = g \summi=0 (1-g X'X)i X'y , \] where li 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.
Abstract
Trenkler [13] described an iteration estimator. This estimator is defined as follows: for 0 < g < 1/li \max \[ \hat{b}m, g = g \summi=0 (1-g X'X)i X'y , \] where li 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.