Generalized inverse estimator and comparison with least squares estimator

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

A new biased estimator based on ridge estimation

Biased regression, Mean squared error, Multicollinearity, Ridge regression, Liu estimator,

Osmotic Pressure and Vasculature of Gingiva in Experimental Diabetes Mellitus

Background: Alterations in tissue osmotic pressure (OP) and vasculature are considered to be the inevitable aspects of an inflammatory process that subsequently alter the fluid dynamics of the tissues involved. The aim of this study was to reveal a profile of OP and vascular changes in periodontally healthy gingival tissues and analyze the relationship between them in diabetes mellitus (DM) to evaluate the possible effects of DM on the fluid dynamics of the periodontium