sampling-minstrata.bib

@article{choudhry:rao:hidiroglou:2012,
    author = {Choudhry, G. Hussain and Rao, J. N. K. and Hidiroglou, Michael A.},
    journal = {Survey Methodology},
    number = {1},
    pages = {23--29},
    title = {On sample allocation for efficient domain estimation},
    volume = {38},
    year = {2012}
}

@Article{neym:1934,
  author    = "Jerzy Neyman",
  year      = "1934",
  title     = "On the Two Different Aspects of the Representative Method:
    The Method of Stratified Sampling and the Method of Purposive Selection",
  journal   = "Journal of the Royal Statistical Society",
  volume    = "109",
  pages     = "558--606"
}

@article{wright:2012,
    abstract =
        {We present a surprising though obvious result that seems to have
        been unnoticed until now. In particular, we demonstrate the
        equivalence of two well-known problems?the optimal allocation of the
        fixed overall sample size n among L strata under stratified random
        sampling and the optimal allocation of the H = 435 seats among the 50
        states for apportionment of the {U.S}. House of Representatives
        following each decennial census. In spite of the strong similarity
        manifest in the statements of the two problems, they have not been
        linked and they have well-known but different solutions; one solution
        is not explicitly exact (Neyman allocation), and the other (equal
        proportions) is exact. We give explicit exact solutions for both and
        note that the solutions are equivalent. In fact, we conclude by
        showing that both problems are special cases of a general problem.
        The result is significant for stratified random sampling in that it
        explicitly shows how to minimize sampling error when estimating a
        total {TY} while keeping the final overall sample size fixed at n;
        this is usually not the case in practice with Neyman allocation where
        the resulting final overall sample size might be near n + L after
        rounding. An example reveals that controlled rounding with Neyman
        allocation does not always lead to the optimum allocation, that is,
        an allocation that minimizes variance.},
    author = {Wright, Tommy},
    doi = {10.1080/00031305.2012.733679},
    journal = {The American Statistician},
    number = {4},
    pages = {217--224},
    title = {The Equivalence of {Neyman} Optimum Allocation for Sampling
        and Equal Proportions for Apportioning the {U.S}. {H}ouse of {R}epresentatives},
    volume = {66},
    year = {2012}
}