Abstract: | Bayesian and empirical Bayesian decision rules are exhibited for the interval estimation of the parameter 0 of a Uniform (0,θ) distribution. The estimate ?,δ>resulting in the interval [?,?+δ]suffers loss given by L(?,δ>,θ)=1-[?≦e≦?+δ]+c1((?-θ)2+(?+δ?θ)2))+c2δ. The solution is presented for prior distributions G which have bounded support, no point masses,∫θ?mdG(θ)<∞ and for some integer m. An example is presented involving a particular parametric form for G and rates of risk convergence in the empirical Bayes problem for this example are calculated. |