Annals of the Institute of Statistical Mathematics

, Volume 41, Issue 3, pp 477–484 | Cite as

Closer estimators of a common mean in the sense of Pitman

  • Tatsuya Kubokawa


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.

Key words and phrases

Pitman closeness common mean Graybill-Deal estimator 


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Copyright information

© The Institute of Statistical Mathematics 1989

Authors and Affiliations

  • Tatsuya Kubokawa
    • 1
  1. 1.Institute of MathematicsUniversity of TsukubaTsukuba, IbarakiJapan

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