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

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.