Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean

V. K. Srivastava and R. S. Singh

Statistics & Probability Letters, 1990, vol. 10, issue 3, 241-245

Abstract: For the estimation of the mean [mu] of a normal population with unknown variance [sigma]2, Searles (1964) provides the minimum mean squared (MMSE) estimator (1 + [sigma]2/(n[mu]2))-1 in the class of all estimators of the type . This MMSE estimator however is not computable in practice if [sigma]/[mu] is unknown. Srivastava (1980) showed that the corresponding computable estimator t = (1 + s2/(n2)) is more efficient than the usual estimator whenever [sigma]2/(n[mu]2) is at least 0.5. However, the gain in efficiency is a function of [mu] and [sigma]2, and therefore remains unknown. This note provides a uniformly minimum variance unbiased estimate of the exact efficiency ratio E(t - [mu])2/E( - [mu])2 to help determine the usefulness of t over in practice.

Keywords: Normal; population; mean; minimum; mean; square; error; exact; efficiency; ratio; uniformly; minimum; variance; unbiased; estimator (search for similar items in EconPapers)
Date: 1990
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Citations: View citations in EconPapers (1)

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