scholarly journals Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

Stat ◽  
2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Hien D. Nguyen
Keyword(s):  
Linear Regression ◽  
Asymptotic Normality ◽  
Least Squares ◽  
Time Domain ◽  
Regression Models ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Linear Regression Models ◽  
Generalized Least Squares Estimator ◽  
The Time Domain

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.

ADDING REGRESSORS TO OBTAIN EFFICIENCY

2009 ◽  
Vol 25 (1) ◽  
pp. 298-301 ◽  
Author(s):  
Sung Jae Jun ◽  
Joris Pinkse
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Efficiency ◽  
Asymptotic Variance ◽  
Generalized Least Squares ◽  
Conditional Heteroskedasticity ◽  
Distributed Data ◽  
Linear Regression Models ◽  
Generalized Least Squares Estimator ◽  
Standard Linear

It is well known that in standard linear regression models with independent and identically distributed data and homoskedasticity, adding “irrelevant regressors” hurts (asymptotic) efficiency unless such irrelevant regressors are orthogonal to the remaining regressors. But we have found that under (conditional) heteroskedasticity “irrelevant regressors” can always be found such that one can achieve the asymptotic variance of the generalized least squares estimator by adding the “irrelevant regressors” to the model.

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