Admissibility of the usual estimators under error-in-variables superpopulation model
AbstractIn 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 32 (1997)
Issue (Month): 3 (March)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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