Question: Let X1, . . . , Xn iid U[ 1 / 2 , + 1 / 2 ], with R unknown. (a) Find a two-dimensional

Let X1, . . . , Xn iid U[ 1/2 , + 1/2 ], with R unknown.

(a) Find a two-dimensional minimal sufficient statistic and show it is minimal.

(b) Show that the minimal sufficient statistic is not complete.

(c) Suppose we want to estimate under the squared error loss L(, d) = ( d) ^2 . The sample mean X (the average of X)seems to be a reasonable estimator of . However, we can improve upon it by Rao-Blackwellizing it. Find this new estimator (X1, . . . , Xn).

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