On risk comparisons of some estimators in a linear regression model under Inagaki’s loss function and nonnormal error terms. (English) Zbl 0937.62611
Summary: We consider the risk performances of some estimators for both location and scale parameters in a linear regression model under Inagaki’s loss function. We prove that the pre-test estimator for location prameter is dominated by the Stein-rule estimator under Inagaki’s loss function when the distribution of error terms is expressed by the scale mixture of normal distribution and the variance of error terms is unknown. It is an extension of the results in Y. Nagata [Ann. Inst. Stat. Math. 35, 365-373 (1983; Zbl 0553.62006)] to our situation. Also we perform numerical calculations to draw the shapes of the risks.
MSC:
| 62J05 | Linear regression; mixed models |
Keywords:
Kullback-Leibler information; Inagaki’s loss function; scale mixture of normal distribution; multivariate \(t\) distribution; pre-test estimator; Stein-rule estimatorCitations:
Zbl 0553.62006References:
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