A theorem on the covariance matrix of a generalized least squares estimator under an elliptically symmetric error

2009 ◽  
Vol 51 (2) ◽  
pp. 389-395 ◽  
Author(s):  
Hiroshi Kurata
Keyword(s):  
Least Squares ◽  
Covariance Matrix ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Generalized Least Squares Estimator

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.

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

scholarly journals Panel Data Estimation for Correlated Random Coefficients Models

Econometrics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Cheng Hsiao ◽  
Qi Li ◽  
Zhongwen Liang ◽  
Wei Xie
Keyword(s):  
Panel Data ◽  
Least Squares ◽  
Asymptotic Properties ◽  
Generalized Least Squares ◽  
Random Coefficients ◽  
Least Squares Estimator ◽  
Finite Sample ◽  
Correlation Pattern ◽  
Panel Data Estimation ◽  
Generalized Least Squares Estimator

This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, the group mean estimator and the generalized least squares estimator. For the group mean estimator, we show that it achieves Chamberlain (1992) semi-parametric efficiency bound asymptotically. For the generalized least squares estimator, we show that when T is large, a generalized least squares estimator that ignores the correlation between the individual coefficients and regressors is asymptotically equivalent to the group mean estimator. In addition, we give conditions where the standard within estimator of the mean of the coefficients is consistent. Moreover, with additional assumptions on the known correlation pattern, we derive the asymptotic properties of panel least squares estimators. Simulations are used to examine the finite sample performances of different estimators.

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