Two-stage sampling schemes arise in survey sampling, especially in situations when the complete update of the frame is difficult. In this paper we solve the problem of fixed precision optimal allocation in two special two-stage sampling schemes. The solution is based on reducing the original question to an eigenvalue problem and then using the Perron-Frobenius theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-5,
author = {Wojciech Niemiro and Jacek Weso\l owski},
title = {Fixed precision optimal allocation in two-stage sampling},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {73-82},
zbl = {1008.62513},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-5}
}
Wojciech Niemiro; Jacek Wesołowski. Fixed precision optimal allocation in two-stage sampling. Applicationes Mathematicae, Tome 28 (2001) pp. 73-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-5/