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A class of efficient and modified testimators for the mean of normal distribution using complete data

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  • Z.A. Al-Hemyari
  • I.H. Hussain
  • A.N. Al-Jobori
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    Abstract

    In this paper, we present a class of efficient simulation and modified shrinkage testimators (ST) for the mean � of normal distribution, when a prior estimate �0 of the mean � is available from the past. The main idea is to incorporate the prior estimate �0 by modifying the standard shrinkage estimator and considering a feasible form of the shrinkage weight function which is used in both of the estimation steps with different quantities, instead of using a shrinkage weight function in the first step of the shrinkage estimator only. The expressions for the bias, mean squared error, and relative efficiency for both cases when σ2 known, or unknown, are derived and studied theoretically and numerically. The resulting testimator dominates the classical estimators in the surprisingly large neighbourhood of the prior estimate �0. The proposed testimator has been also compared favourably with the existing shrinkage estimators. The discussions regarding the usefulness of these testimators under different situations are provided as conclusions from the various numerical tables obtained from simulation results. Two applications of real data have demonstrated that the method is versatile and not computationally demanding.

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    Bibliographic Info

    Article provided by Inderscience Enterprises Ltd in its journal Int. J. of Data Analysis Techniques and Strategies.

    Volume (Year): 3 (2011)
    Issue (Month): 4 ()
    Pages: 406-425

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    Handle: RePEc:ids:injdan:v:3:y:2011:i:4:p:406-425

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    Web page: http://www.inderscience.com/browse/index.php?journalID=282

    Related research

    Keywords: normal distribution; complete data; shrinkage; modified testimators; simulation; pretest region; bias ratio; relative efficiency.;

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