Abstract
In this paper, we consider a heteroscedastic linear regression model with omitted variables. We derive the density function of the pre-test estimator consisting of the two-stage Aitken estimator (2SAE) and the ordinary least squares estimator (OLSE) after the pre-test for homoscedasticity. We also derive the first two moments based on the density function and show the sufficient condition for the pre-test estimator to dominate the 2SAE in terms of the MSE. Our numerical evaluations show that when this sufficient condition does not hold and when the magnitude of the specification error is large, the pre-test estimator can be dominated by the 2SAE, and further, the 2SAE can be dominated by the OLSE.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adjibolosso, S.B.-S.K. (1991), “On Choosing the Levels of Significance for the Goldfeld and Quandt Heteroskedasticity Pretesting,”Communications in Statistics—Simulation and Computation, 20, 437–447.
Giles, D.E.A. (1992), “The Exact Distribution of a Simple Pre-Test Estimator,”Readings in Econometric Theory and Practice, A Volume in Honor of George Judge, W. Griffiths, H. Lütkepohl and M.E. Bock (Eds.), North Holland: Amsterdam, 57–74.
Giles, D.E.A. and Srivastava, V.K. (1993), “The Exact Distribution of a Least Squares Regression Coefficient Estimator After a Preliminary t-Test,”Statistics & Probability Letters, 16, 59–64.
Greenberg, E. (1980), “Finite Sample Moments of a Preliminary Test Estimator in the Case of Possible Heteroscedasticity,”Econometrica, 48, 1085–1813.
Mandy, D.M. (1984), “The Moments of a Pre-Test Estimator Under Possible Heteroscedasticity,”Journal of Econometrics, 25, 29–33.
Ohtani, K. (1993a), “The Density Function of the Pre-Test Estimator in a Linear Regression Model Under Possible Heteroscedasticity,”Kokumin-Keizai Zasshi (Journal of Economics and Business Administration, 168, 27–37, in Japanese).
Ohtani, K. (1993b), “The Exact Distribution and Density Functions of the Stein-Type Estimator for Normal Variance,”Communications in Statistics— Theory and Methods, 22, 2863–2876.
Ohtani, K., Giles, D.E.A. and Giles, J.A. (1993), “The Risk Behavior of a Pre-Test Estimator in a Linear Regression Model with Possible Heteroscedasticity Under the LINEX Loss Function,” Discussion Paper #9307, Department of Economics, University of Canterbury.
Ohtani, K. and Kakimoto, S. (1987), “Small Sample Properties of the Two-Stage Aitken Predictor Under Specification Error,”Journal of the Japan Statistical Society, 17, 119–128.
Ohtani, K. and Toyoda, T. (1980), “Estimation of Regression Coefficients After a Preliminary Test for Homoscedasticity,”Journal of Econometrics, 12, 151–159.
Özcam, A. and Judge, G.G. (1991), “Some Risk Results for a Two-Stage Pre-Test Estimator in the Case of Possible Heteroskedasticity,”Journal of Econometrics, 48, 355–371.
Taylor, W.E. (1978), “The Heteroscedastic Linear Model: Exact Finite Sample Results,”Econometrica, 46, 663–675.
Yancey, T.A., Judge, G.G. and Miyazaki, S. (1984), “Some Improved Estimators in the Case of Possible Heteroscedasticity,”Journal of Econometrics, 25, 133–150.
Author information
Authors and Affiliations
Additional information
We are extremely grateful to David Giles and an anonymous referee for their helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Ohtani, K., Giles, J.A. The density function and the MSE dominance of the pre-test estimator in a heteroscedastic linear regression model with omitted variables. Statistical Papers 37, 323–342 (1996). https://doi.org/10.1007/BF02926112
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02926112