Abstract
Consider the problem of estimating the common mean of two normal populations with different unknown variances. Suppose a random sample of sizem is drawn from the first population and a random sample of sizen is drawn from the second population. The paper gives a family of estimators closer than the sample mean of the first population in the sense of Pitman (1937,Proc. Cambridge Phil. Soc.,33, 212–222). In particular, the Graybill-Deal estimator (1959,Biometrics,15, 543–550) is shown to be closer than each of the sample means ifm≥5 andn≥5.
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Kubokawa, T. Closer estimators of a common mean in the sense of Pitman. Ann Inst Stat Math 41, 477–484 (1989). https://doi.org/10.1007/BF00050663
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DOI: https://doi.org/10.1007/BF00050663