Estimating the error variance after a pre-test for an inequality restriction on the coefficients |
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| Institution: | 1. Institut für Geowissenschaften, Universität Heidelberg, Germany,;2. John de Laeter Centre, Curtin University, Australia;3. Department of Earth, Planetary, and Space Sciences, University of California, United States,;4. Institut für Geowissenschaften, Goethe Universität Frankfurt am Main, Germany;5. Frankfurt Isotope and Element Research Center (FIERCE), Goethe University, Frankfurt, Germany |
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| Abstract: | Estimation of the regression error variance after a preliminary test of an inequality constraint on the coefficient vector is considered. We derive the exact finite sample risk of several inequality restricted and pre-test estimators of σ2. These estimators are associated with the maximum likelihood, least squares and minimum mean squared error component estimators. Optimal critical values for the pre-test according to a mini-max regret criterion are numerically calculated. Furthermore, we examine the robustness of the optimal choice of critical values and the risk properties of the estimators of σ2 to model mis-specification through the exclusion of relevant regressors. |
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