A problem of minimax estimation with directional information

This problem is in the area of minimax selection of experiments. Nature chooses a number [theta] in the closed interval [-1, 1]. The statistician chooses a number y in the same interval (an experiment) and is informed whether [theta] < y, [theta] = y, or 0> y. Based on this information, the statistician then estimates [theta] with squared error loss. The minimax solution of this problem is found. The minimax value is 1/(2e). The least favorable distribution involves the truncated t-distribution with two degrees of freedom. The minimax choice of experiment involves the truncated t-distribution with zero degrees of freedom.