Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances. (English) Zbl 0745.62067
Summary: We derive the exact risk (under quadratic loss) of pre-test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances. The pre-test in question is one of the validity of a set of exact linear restrictions on the model’s coefficient vector. We demonstrate how the known results for the model with normal disturbances can be extended to this broader case. We also show that the critical value of unity results in a minimum of the risk of the pre-test estimator of the error variance. To illustrate the results we assume multivariate Student-\(t\) regression disturbances and numerically evaluate the derived expressions.
MSC:
| 62J05 | Linear regression; mixed models |
| 62F10 | Point estimation |
| 62H12 | Estimation in multivariate analysis |
| 62P20 | Applications of statistics to economics |
| 62F03 | Parametric hypothesis testing |
Keywords:
exact risk; quadratic loss; pre-test estimators; prediction vector; error variance; spherically symmetric disturbances; exact linear restrictions; normal disturbances; multivariate Student-\(t\) regression disturbancesSoftware:
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