A sufficient condition for the MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated in a misspecified linear regression model

2018 ◽  
Vol 88 (11) ◽  
pp. 2034-2047
Author(s):  
Akio Namba ◽  
Haifeng Xu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Coefficient ◽  
Shrinkage Estimator ◽  
Sufficient Condition ◽  
Positive Part

A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model

1993 ◽  
Vol 9 (4) ◽  
pp. 668-679 ◽  
Author(s):  
Kazuhiro Ohtani
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Numerical Computation ◽  
Linear Regression Model ◽  
Exact Formula ◽  
Sufficient Condition ◽  
Omitted Variables ◽  
Specification Error ◽  
Positive Part ◽  
Predictive Risk

In this paper, we examine the performance of the predictive risk of the Steinrule (SR) and positive-part Stein-rule (PSR) estimators when relevant regressors are omitted in the specified model. The exact formula of the predictive risk of the PSR estimator is derived, and the sufficient condition for the PSR estimator to dominate the SR estimator under a specification error is given. It is shown by numerical computation that the PSR estimator seems to be the best choice among the OLS, SR, and PSR estimators even when there are omitted variables.

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.

Sign in / Sign up

Export Citation Format

Share Document