Performance of Preliminary Test Estimators for Error Variance Based on W, LR and LM Tests

2019 ◽  
Vol 33 (4) ◽  
pp. 1200-1211
Author(s):  
Guikai Hu ◽  
Jinguan Lin
Keyword(s):  
Preliminary Test ◽  
Error Variance ◽  
Lm Tests

scholarly journals On the Size Corrected Tests in Improved Estimation

2005 ◽  
Vol 57 (3-4) ◽  
pp. 143-160
Author(s):  
Z. Hoque ◽  
B. Billah ◽  
S. Khan
Keyword(s):  
Degrees Of Freedom ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Preliminary Test ◽  
Error Variance ◽  
Lagrangian Multiplier ◽  
Significance Level ◽  
Lm Tests ◽  
Coefficient Vector ◽  
Asymptotic Tests

In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald ( W), likelihood ratio ( LR) and Lagrangian multiplier ( LM) tests. The correction factors used are those obt,ained from degrees of freedom corrections to the estimate of the error variance and those obtained from the second­order Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) fun ctions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three t ests are based on the same asymptotic chi­square critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.

scholarly journals Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors

2020 ◽  
Vol 15 (1) ◽  
pp. 27-43
Author(s):  
Jianwen Xu ◽  
Hu Yang
Keyword(s):  
Regression Model ◽  
Sufficient Conditions ◽  
Preliminary Test ◽  
Multiple Regression Model ◽  
Regression Coefficients ◽  
Lagrangian Multiplier ◽  
Ridge Estimator ◽  
Lm Tests ◽  
Theoretical Results ◽  
Almost Unbiased

In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.

scholarly journals Preliminary-Test Estimation of the Error Variance in Linear Regression

1987 ◽  
Vol 3 (2) ◽  
pp. 299-304 ◽  
Author(s):  
Judith A. Clarke ◽  
David E. A. Giles ◽  
T. Dudley Wallace
Keyword(s):  
Linear Regression ◽  
Mean Squared Error ◽  
Preliminary Test ◽  
Error Variance ◽  
Error Component ◽  
Quadratic Loss ◽  
Finite Sample ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Preliminary Test Estimation

We derive exact finite-sample expressions for the biases and risks of several common pretest estimators of the scale parameter in the linear regression model. These estimators are associated with least squares, maximum likelihood and minimum mean squared error component estimators. Of these three criteria, the last is found to be superior (in terms of risk under quadratic loss) when pretesting in typical situations.

scholarly journals Estimating the error variance in regression after a preliminary test of restrictions on the coefficients

1987 ◽  
Vol 34 (3) ◽  
pp. 293-304 ◽  
Author(s):  
Judith A. Clarke ◽  
David E.A. Giles ◽  
T.Dudley Wallace
Keyword(s):  
Preliminary Test ◽  
Error Variance
Sign in / Sign up

Export Citation Format

Share Document