Some comments on: Özkale, M.R., Kaciranlar, K. (2008): Comparisons of the r–k class estimator to the ordinary least squares estimator under the Pitman’s closeness criterion. Statistical Papers, 49:503–512

2010 ◽  
Vol 53 (2) ◽  
pp. 497-503 ◽  
Author(s):  
Wenxue Li ◽  
Hu Yang ◽  
Jibo Wu
Keyword(s):  
Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Ordinary Least Squares Estimator ◽  
Pitman’S Closeness Criterion

scholarly journals Comparison of Two Estimators of the Regression Coefficient Vector Under Pitman’s Closeness Criterion

2020 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Squared Error ◽  
Ordinary Least Squares Estimator ◽  
Mixed Estimator ◽  
Coefficient Vector ◽  
The Mean ◽  
Pitman’S Closeness Criterion

Schaffrin and Toutenburg [1] proposed a weighted mixed estimation based on the sample information and the stochastic prior information, and they also show that the weighted mixed estimator is superior to the ordinary least squares estimator under the mean squared error criterion. However, there has no paper to discuss the performance of the two estimators under the Pitman’s closeness criterion. This paper presents the comparison of the weighted mixed estimator and the ordinary least squares estimator using the Pitman’s closeness criterion. A simulation study is performed to illustrate the performance of the weighted mixed estimator and the ordinary least squares estimator under the Pitman’s closeness criterion.

ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS

2002 ◽  
Vol 18 (5) ◽  
pp. 1121-1138 ◽  
Author(s):  
DONG WAN SHIN ◽  
MAN SUK OH
Keyword(s):  
Least Squares ◽  
Asymptotic Efficiency ◽  
Characteristic Root ◽  
Sufficient Conditions ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Least Squares Estimator ◽  
Characteristic Roots ◽  
Generalized Least Squares Estimator ◽  
Ordinary Least Squares Estimator

For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (ΓX = XC + V for some matrix C) for V asymptotically dominated by X, which is analogous to the condition (ΓX = XC for some matrix C) for numerical equivalence of the OLSE and the GLSE.

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