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Admissibility of the usual estimators under error-in-variables superpopulation model. (English) Zbl 0874.62005

Summary: We first point out that a result in P. Mukhopadhyay [J. Stat. Plann. Inference 41, No. 2, 151-161 (1994; Zbl 0798.62018)] on the optimality of the usual estimator \(s^2_y\) of finite population variance is not true. We then give a necessary and sufficient condition for \(((1-f)/n)s^2_y\) (where \(f\) means the sampling fraction) as the estimator of the precision of the sample mean \(\overline{y}_s\) 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 \(((1-f)/n)((n-1)/(n+1))s^2_y\) over \(((1-f)/n)s^2_y\) under the usual superpopulation model without measurement errors is admissible in the class of quadratic estimators.

MSC:

62D05 Sampling theory, sample surveys
62C15 Admissibility in statistical decision theory

Citations:

Zbl 0798.62018
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References:

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