Title: Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean
Abstract: Abstract For the estimation of the mean μ of a normal population with unknown variance σ2, Searles (1964) provides the minimum mean squared (MMSE) estimator (1 + σ2/(nμ2))−1 x in the class of all estimators of the type x . This MMSE estimator however is not computable in practice if σ/μ is unknown. Srivastava (1980) showed that the corresponding computable estimator t = (1 + s2/(n x 2)) x is more efficient than the usual estimator x whenever σ2/(nμ2) is at least 0.5. However, the gain in efficiency is a function of μ and σ2, and therefore remains unknown. This note provides a uniformly minimum variance unbiased estimate of the exact efficiency ratio E(t − μ)2/E( x − μ)2 to help determine the usefulness of t over x in practice.
Publication Year: 1990
Publication Date: 1990-08-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 8
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