Risk comparison of improved estimators in a linear regression model with multivariate $$t$$ errors under balanced loss function.(English)Zbl 1437.62258

Summary: Under a balanced loss function, we derive the explicit formulae of the risk of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariate $$t$$ errors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariate $$t$$ errors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

MSC:

 62J05 Linear regression; mixed models 62J07 Ridge regression; shrinkage estimators (Lasso) 62H12 Estimation in multivariate analysis
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References:

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