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

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 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.

Measuring the Big Five in Self-Report and Other Ratings

2000 ◽  
Vol 16 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Claudio Barbaranelli ◽  
Gian Vittorio Caprara
Keyword(s):  
Big Five ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Error Variance ◽  
The Self ◽  
Self Report ◽  
Sources Of Information ◽  
Third Person ◽  
Fit Indexes ◽  
Response Modes

Summary: The aim of the study is to assess the construct validity of two different measures of the Big Five, matching two “response modes” (phrase-questionnaire and list of adjectives) and two sources of information or raters (self-report and other ratings). Two-hundred subjects, equally divided in males and females, were administered the self-report versions of the Big Five Questionnaire (BFQ) and the Big Five Observer (BFO), a list of bipolar pairs of adjectives ( Caprara, Barbaranelli, & Borgogni, 1993 , 1994 ). Every subject was rated by six acquaintances, then aggregated by means of the same instruments used for the self-report, but worded in a third-person format. The multitrait-multimethod matrix derived from these measures was then analyzed via Structural Equation Models according to the criteria proposed by Widaman (1985) , Marsh (1989) , and Bagozzi (1994) . In particular, four different models were compared. While the global fit indexes of the models were only moderate, convergent and discriminant validities were clearly supported, and method and error variance were moderate or low.

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