Lindley Type Estimators When the Norm is Restricted to an Interval

Consider the problem of estimating a mean vector under the quadratic loss, based on a sample , , , . We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm is restricted to a known interval, where and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.