Abstract
This problem is in the area of minimax selection of experiments. Nature chooses a number θ in the closed interval [−1, 1]. The statistician chooses a number y in the same interval (an experiment) and is informed whether θ < y, θ = y, or 0 > y. Based on this information, the statistician then estimates θ with squared error loss. The minimax solution of this problem is found. The minimax value is 1/(2 e). 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.
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