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

✍ Scribed by Guohua Zou; Hua Liang

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 382 KB
• Volume: 32
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00087-9

✦ Synopsis

In this paper, we first point out that a result in Mukhopadhyay (1994) on the optimality of the usual estimator s 2 of 2 (wherefmeans finite population variance is not true. We then give a necessary and sufficient condition for ((1 -f)/n) sy the sampling fraction) as the estimator of the precision of the sample mean ~7, to be admissible in the class of quadratic estimators. Our result shows that there is virtual difference between the admissibility of estimators under error-invariables superpopulation model and the usual superpopulation model. We also show that the improved estimator 2 ((I -f)/n) ((n -1)/(n + 1)) sy over ((1 -f)/n) s 2 under the usual superpopulation model without measurement errors is admissible in the class of quadratic estimators.