On truncation of shrinkage estimators in simultaneous estimation of normal means
In estimating a multivariate normal mean θ = (θ1, …, θk)t under sum of squares error loss, it is well known that Stein estimators improve upon the usual estimator (in terms of expected loss) if k ≥ 3. The improvement obtained is significant, however, only if the θi are fairly close to the point towards which the Stein estimator shrinks. When extreme θi are likely (such as when the θi are thought to arise from a possibly heavy-tailed prior distribution), the standard Stein estimators may offer little improvement over the usual estimator. Stein (1981) proposed a limited translation Stein estimator to correct this deficiency. This estimator is analyzed herein for a number of heavy-tailed prior distributions. An adaptive version of the estimator is also discussed. © 1983 Taylor & Francis Group, LLC.
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