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

Author

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  • Srivastava, V. K.
  • Singh, R. S.

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.

Suggested Citation

  • Srivastava, V. K. & Singh, R. S., 1990. "Uniformly minimum variance unbiased estimator of efficiency ratio in estimation of normal population mean," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 241-245, August.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:3:p:241-245
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    Cited by:

    1. Warisa Thangjai & Suparat Niwitpong & Sa-Aat Niwitpong, 2017. "Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation," Mathematics, MDPI, vol. 5(3), pages 1-23, July.

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