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Admissibility of the usual estimators under error-in-variables superpopulation model

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  • Zou, Guohua
  • Liang, Hua

Abstract

In this paper, we first point out that a result in Mukhopadhyay (1994) on the optimality of the usual estimator sy2 of finite population variance is not true. We then give a necessary and sufficient condition for ((1 - f)/n) sy2 (where f means the sampling fraction) as the estimator of the precision of the sample mean s to be admissible in the class of quadratic estimators. Our result shows that there is virtual difference between the admissibility of estimators under error-in-variables superpopulation model and the usual superpopulation model. We also show that the improved estimator ((1 - f)/n) ((n - 1)/(n + 1)) sy2 over ((1 - f)/n) sy2 under the usual superpopulation model without measurement errors is admissible in the class of quadratic estimators.

Suggested Citation

  • Zou, Guohua & Liang, Hua, 1997. "Admissibility of the usual estimators under error-in-variables superpopulation model," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 301-309, March.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:3:p:301-309
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