This article proposes a bootstrap procedure for estimating the risk minimizing decision-rule from within a parameterized family of rules. The procedure is conceptually simple and applicable to a broad class of decision problems involving parameter uncertainty. Moreover, when applied to Markowitz's (1952) model of portfolio selection—a leading example in which parameter uncertainty arises—it is shown to be capable of generating decision rules with lower risk than estimators derived from conventional methods. Theoretical results establishing the asymptotic optimality of the procedure are also presented.

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