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A class of admissible estimators of a finite population total

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Summary

In order to estimate the total value of an attribute of a finite population, Brewer [2] proposed an estimator which is asymptotically design-unbiased and which is optimal with respect to a certain superpopulation model. In this note, it is shown that a class of estimators which includes Brewer's estimator, as well as the usual ratio estimator, is admissible for any fixed population size. The proof of the result follows that of Joshi [4], [5].

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References

  1. Basu, D. (1971). An essay on the logical foundations of survey sampling, part one,Foundations of Statistical Inference (eds. V. P. Godambe and D. A. Sprott), Holt, Rinehart and Winston, Toronto, 203–233.

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  2. Brewer, K. R. W. (1979). A class of robust sampling designs for large scale surveys,J. Amer. Statist. Ass.,74, 911–915.

    Article  MathSciNet  Google Scholar 

  3. Hodges, J. L., Jr. and Lehmann, E. L. (1951). Some applications of the Cramér-Rao inequality,Proc. Second Berkeley Symp. Math. Statist. Prob., University of California Press, 13–22.

  4. Joshi, V. M. (1965). Admissibility and Bayes estimation in sampling finite populations, III,Ann. Math. Statist.,36, 1723–1729.

    Article  MathSciNet  Google Scholar 

  5. Joshi, V. M. (1966). Admissibility and Bayes estimation in sampling finite populations, IV,Ann. Math. Statist. 37, 1658–1670.

    Article  MathSciNet  Google Scholar 

  6. Joshi, V. M. (1979). Joint admissibility of the sample means as estimators of the means of finite populations.Ann. Statist.,7, 995–1002.

    Article  MathSciNet  Google Scholar 

  7. Meeden, G. and Ghosh, M. (1983). Choosing between experiments: applications to finite population sampling,Ann. Statist.,11, to appear.

    Article  MathSciNet  Google Scholar 

  8. Robinson, P. M. and Tsui, K. W. (1981). Optimal asymptotically design-unbiased estimation of a population total,Technical Report No. 634, Dept. of Statistics, Univ. of Wisconsin-Madison.

  9. Royall, R. M. (1970). On finite population sampling theory under certain linear regression models.Biometrika,64, 499–513.

    MATH  Google Scholar 

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Authors and Affiliations

  1. University of Wisconsin-Madison, Madison, USA

    K. W. Tsui

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  1. K. W. Tsui
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Tsui, K.W. A class of admissible estimators of a finite population total. Ann Inst Stat Math 35, 25–30 (1983). https://doi.org/10.1007/BF02480960

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  • DOI: https://doi.org/10.1007/BF02480960

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