论文标题
解决最佳分配问题的另一个解决方案
Another Solution for Some Optimum Allocation Problem
论文作者
论文摘要
我们得出了分层采样中最佳样品分配问题的最佳条件，该分层采样的确定为确定固定地层样本大小，以最大程度地减少调查的总成本，这是在分层$π$估算器的假定差异水平下，人口总数（或均值）总数（或平均值）和单侧的上限在Strata中占样本大小。在这种情况下，我们假定方差函数是某种通用形式的，尤其是涵盖了层次中的简单随机抽样的情况，而层次中则没有替换设计。上述最佳条件将来自Karush-Kuhn-Tucker条件。基于既定的最佳条件，我们提供了现有过程的最优性的正式证明，该过程称为LRNA，该过程解决了所考虑的分配问题。我们以这样的方式制定了LRNA，以便在单方面的下限下在地层中的样本量施加的单侧下限下提供了经典的最佳分配问题（即，在固定总成本下的估计量方差最小化）。在这种情况下，可以将LRNA视为与流行的递归Neyman分配程序的对方，该过程用于解决最佳样品分配的经典问题，并增加了一个单方面的上限。可以通过我们的Stratallo软件包获得LRNA的现成R-IMPLENTION，该软件包可在综合R档案网络（CRAN）软件包存储库上发布。
We derive optimality conditions for the optimum sample allocation problem in stratified sampling, formulated as the determination of the fixed strata sample sizes that minimize the total cost of the survey, under the assumed level of variance of the stratified $π$ estimator of the population total (or mean) and one-sided upper bounds imposed on sample sizes in strata. In this context, we presume that the variance function is of some generic form that, in particular, covers the case of the simple random sampling without replacement design in strata. The optimality conditions mentioned above will be derived from the Karush-Kuhn-Tucker conditions. Based on the established optimality conditions, we provide a formal proof of the optimality of the existing procedure, termed here as LRNA, which solves the allocation problem considered. We formulate the LRNA in such a way that it also provides the solution to the classical optimum allocation problem (i.e. minimization of the estimator's variance under a fixed total cost) under one-sided lower bounds imposed on sample sizes in strata. In this context, the LRNA can be considered as a counterparty to the popular recursive Neyman allocation procedure that is used to solve the classical problem of an optimum sample allocation with added one-sided upper bounds. Ready-to-use R-implementation of the LRNA is available through our stratallo package, which is published on the Comprehensive R Archive Network (CRAN) package repository.
