Geodesic
Non-Existence of Estimates of Prescribed Accuracy in Fixed Sample Size
Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 135-139

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Let X be a random variable whose density (or distribution if discrete) f(x; θ) depends on an unknown parameter θ, real or vector-valued. By making observations on X we want to know whether there exist estimates of prescribed accuracy for the real-valued parametric function g(θ). By an estimate of prescribed accuracy for g(θ) we mean a confidence interval of prescribed length and confidence coefficient or a point estimate with prescribed expected loss W. In the following our loss functions W will always satisfy the requirement that W(δ, θ) = V(|δ - θ|), where V is a strictly increasing function of its argument. The class of such loss functions includes among others the squared error loss. 
Singh, Rajinder. Non-Existence of Estimates of Prescribed Accuracy in Fixed Sample Size. Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 135-139. doi: 10.4153/CMB-1968-016-0
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