Estimating the Common Mean of Several Normal Populations
Norwood, Thomas E. ; Hinkelmann, Klaus
Ann. Statist., Tome 5 (1977) no. 1, p. 1047-1050 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For $x_i \sim N(\mu, \sigma_i^2) (i = 1, 2,\cdots, n)$ and the $x_i$'s independent, this paper gives necessary and sufficient conditions under which the weighted average of the $x_i$'s, with weights proportional to inverses of the sample variances, has uniformly smaller variance than any of the $x_i$'s.
Publié le : 1977-09-14
Classification:  Normal populations,  common mean,  different unknown variances,  estimation,  weighted average of sample means,  62F10 
@article{1176343959,
     author = {Norwood, Thomas E. and Hinkelmann, Klaus},
     title = {Estimating the Common Mean of Several Normal Populations},
     journal = {Ann. Statist.},
     volume = {5},
     number = {1},
     year = {1977},
     pages = { 1047-1050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343959}
}

Norwood, Thomas E.; Hinkelmann, Klaus. Estimating the Common Mean of Several Normal Populations. Ann. Statist., Tome 5 (1977) no. 1, pp.  1047-1050. http://gdmltest.u-ga.fr/item/1176343959/