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Double stage estimation of population variance

  • B. N. Pandey
Article

Summary

Consider a normal population with mean μ and variance σ2. We are interested in the estimation of population variance with the help of guess value σ 0 2 and a sample of observations. In this paper, a double stage shrinkage estimator\(\hat \sigma _k^2 \) based on the shrinkage estimatorks 1 2 +(1-k 0 2 ifs 1 2 R and the usual estimator\(s^2 = \frac{{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2 }}{{n_1 + n_2 - 2}}\) ifs 1 2 R, whereR is some specified region, have been proposed. The expressions for bias and mean squared error have been obtained. Comparison with the usual estimators2 have been made. It was found that though the largest gain is obtained fork=0, we can use\(\hat \sigma _k^2 \) with 0≦k≦1/2 even when σ2 is very close to σ 0 2

Keywords

Shrinkage Normal Population Population Variance Usual Estimator Large Gain 

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References

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    Arnold, J. C. and Bayyatti, Al. H. A. (1970). On double stage estimation of the mean using prior knowledge,Biometrics,26, 787–800.MathSciNetCrossRefGoogle Scholar
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    Pearson, E. S. and Hartley, H. A. (1939).The Biomerika Tables, Cambridge University Press, London.Google Scholar
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    Pandey, B. N. and Singh, J. (1977). Estimation of variance of normal population using prior information.J. Indian Statist. Ass.,15, 141–150.MathSciNetGoogle Scholar
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    Thompson, J. R. (1968). Some shrinkage techniques for estimating the mean,J. Amer. Statist. Ass.,63, 113–123.MathSciNetGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • B. N. Pandey
    • 1
  1. 1.Banarasu Hindu UniversityIndia

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