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Improved estimation of the mean in one-parameter exponential families with known coefficient of variation

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Abstract

The value for which the mean square error of a biased estimatoraT for the mean μ is less than the variance of an unbiased estimatorT is derived by minimizingMSE(aT). The resulting optimal value is 1/[1+c(n)v 2], wherev=σ/μ, is the coefficient of variation. WhenT is the UMVUE\(\bar X\), thenc(n)=1/n, and the optimal value becomes 1/(n+v 2) (Searls, 1964). Whenever prior information about the size ofv is available the shrinkage procedure is useful. In fact for some members of the one-parameter exponential families it is known that the variance is at most a quadratic function of the mean. If we identify the pertinent coefficients in the quadratic function, it becomes easy to determinev.

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Authors and Affiliations

  1. Department of Statistics, Addis Ababa University, Ethiopia

    E. Wencheko

  2. Department of Statistics and Computer Science, University of Peradeniya, Sri Lanka

    P. Wijekoon

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  1. E. Wencheko
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  2. P. Wijekoon
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Wencheko, E., Wijekoon, P. Improved estimation of the mean in one-parameter exponential families with known coefficient of variation. Statistical Papers 46, 101–115 (2005). https://doi.org/10.1007/BF02762037

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  • DOI: https://doi.org/10.1007/BF02762037

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