| dc.description.abstract |
In this paper we derive and present optimal critical points for pre-tests in regression
using a minimum average relative risk criterion. We use the same type risk functions
as Sawa and Hiromatsu [8] who, in a recent paper in this journal, derived pre-test
critical values using a minimax regret criterion. Since James-Stein type estimators
can be shown to dominate any pre-test estimator for the risk functions used here and
in [8], no normative claims are made for the critical values we give. However, the
use of pre-testing procedures continues in practice and the results given here, contrasted
with other results, add to information about the character of costs and returns to
such practices.
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