17 research outputs found

    Generalized inverse estimator and comparison with least squares estimator

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    Trenkler [13] described an iteration estimator. This estimator is defined as follows: for 0<γ<1/λi0 < \gamma < 1/\lambda_i max β^m,γ=γi=0m(1γXX)iXy\hat{\beta}_{m,\gamma}=\gamma\sum\limits_{i=0}^m(1- \gamma X' X)^iX'y where λi\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<γ<1/λi0 < \gamma < 1/\lambda_i max β^m,γ=γi=0m(1γXX)iXy\hat{\beta}_{m,\gamma}=\gamma\sum\limits_{i=0}^m(1- \gamma X' X)^iX'y where λi\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

    Osmotic Pressure and Vasculature of Gingiva in Experimental Diabetes Mellitus

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    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
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