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The Exact Risks of Some Pre-Test and Stein-Type Regression Estimators Under Balanced Loss

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  • Giles, Judith A.
  • Giles, David E. A.
  • Ohtani, Kazuhiro

Abstract

In regression analysis we are often interested in using an estimator which is "precise" and which simultaneously provides a model with "good fit". In this paper we consider the risk properties of several estimators of the regression coefficient vector under "balanced" loss. This loss function (Zellner (1991)) reflects both of the above attributes. Under a particular form of balanced loss, we derive the predictive risk of the pre-test estimator which results after a test for exact linear restrictions on the coefficient vector. The corresponding risks of a Stein-rule and positive-part Stein-rule estimators are also established. The risks based on loss functions which allow only for estimation precision, or only for goodness of fit, are special cases of our results, and we draw appropriate comparisons. In particular, we show that some of the well-known results under (quadratic) precision-only loss are not robust to our generalisation of the loss function.

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Handle: RePEc:ags:canzdp:263725
DOI: 10.22004/ag.econ.263725
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