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

Published online by Cambridge University Press:  20 November 2018

Rajinder Singh
Rajinder Singh*
Affiliation:
University of Saskatchewan and S.R.I. Canadian Math. Congress, Edmonton, Alberta
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 135 - 139
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Singh, R., (1963), Existence of bounded length confidence intervals. Ann. Math. Statist. 34,1474-1485.10.1214/aoms/1177703879Google Scholar
2. Scheffe, H., (1947), A useful convergence theorem for probability distributions. Ann. Math. Statist. 18, 434-438.Google Scholar
3. Zacks, S., (1966), Sequential estimation of the mean of a log-normal distribution having a prescribed proportional closeness. Ann. Math. Statist. 37, 1688-1696.10.1214/aoms/1177699158Google Scholar
4. Zacks, S., (1967), On the non-existence of a fixed sample estimator of the mean of a log-normal distribution having a prescribed proportional closeness. Ann. Math. Statist. 38, 949.Google Scholar