scholarly journals Estimation of mean squared error of model-based estimators of small area means under a nested error linear regression model

2013 ◽  
Vol 117 ◽  
pp. 76-87 ◽  
Author(s):  
Mahmoud Torabi ◽  
J.N.K. Rao
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Small Area ◽  
Mean Squared Error ◽  
Model Based ◽  
Squared Error

scholarly journals Risk Comparison of Improved Estimators in a Linear Regression Model with MultivariatetErrors under Balanced Loss Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guikai Hu ◽  
Qingguo Li ◽  
Shenghua Yu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Loss Function ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Balanced Loss Function ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Improved Estimators

Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariateterrors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariateterrors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

scholarly journals On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

City Manager Compensation and Performance

2013 ◽  
pp. 325-332
Author(s):  
Jean X. Zhang
Keyword(s):  
Neural Network ◽  
Linear Regression ◽  
Regression Model ◽  
Nonlinear Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
City Manager ◽  
Squared Error ◽  
And Performance ◽  
Manager Compensation

This chapter proposes a nonlinear artificial Higher Order Neural Network (HONN) model to study the relation between manager compensation and performance in the governmental sector. Using a HONN simulator, this study analyzes city manager compensation as a function of local government performance, and compares the results with those from a linear regression model. This chapter shows that the nonlinear model generated from HONN has a smaller Root Mean Squared Error (Root MSE) of 0.0020 as compared to 0.06598 from a linear regression model. This study shows that artificial HONN is an effective tool in modeling city manager compensation.

scholarly journals PMSE PERFORMANCE OF THE BIASED ESTIMATORS IN A LINEAR REGRESSION MODEL WHEN RELEVANT REGRESSORS ARE OMITTED

2002 ◽  
Vol 18 (5) ◽  
pp. 1086-1098 ◽  
Author(s):  
Akio Namba
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Positive Part ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Explicit Formulae ◽  
Biased Estimators

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

scholarly journals Two Classes of Almost Unbiased Type Principal Component Estimators in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yalian Li ◽  
Hu Yang
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Principal Component ◽  
Monte Carlo Simulation Study ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Almost Unbiased

This paper is concerned with the parameter estimator in linear regression model. To overcome the multicollinearity problem, two new classes of estimators called the almost unbiased ridge-type principal component estimator (AURPCE) and the almost unbiased Liu-type principal component estimator (AULPCE) are proposed, respectively. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a Monte Carlo simulation study is given to illustrate the performance of the proposed estimators.

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