Generalized Inverse Estimator and comparison with Least Squares Estimator

Authors: S. Sakallıoğlu, F. Akdeniz

Abstract: Trenkler [13] described an iteration estimator. This estimator is defined as follows: for $0 < \gamma < 1/\lambda_i \max$ \[ \hat{\beta}_{m, \gamma} = \gamma \sum^m_{i=0} (1-\gamma X'X)^i X'y , \] 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.


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