Non-Existence of Estimates of Prescribed Accuracy in Fixed Sample Size

Extract

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.