An exact algorithm for the stratification problem with proportional allocation

Abstract

We report a new optimal resolution for the statistical stratification problem under proportional sampling allocation among strata. Consider a finite population of N units, a random sample of n units selected from this population and a number L of strata. Thus, we have to define which units belong to each stratum so as to minimize the variance of a total estimator for one desired variable of interest in each stratum, and consequently reduce the overall variance for such quantity. In order to solve this problem, an exact algorithm based on the concept of minimal path in a graph is proposed and assessed. Computational results using real data from IBGE (Brazilian Central Statistical Office) are provided.

Heuristic algorithm for univariate stratification problem

“…In [8], an exact algorithm based on concepts of graph theory and the minimization of the expression of variance and application of proportional allocation is proposed. In [36], a comparative study between the algorithm proposed in [35,37] and the algorithm proposed in [30] is presented.…”

“…Before detailing the proposed heuristic, the discretization also considered in [8,10] will be presented and used as a basis for representing the solutions produced by the heuristic. The discretization consists of considering only feasible candidates to cutoff points the ones available in 𝑋 𝑈 without repetition.…”

Comparison of the Efficiency of the Various Algorithms in Stratified Sampling when the Initial Solutions are Determined with Geometric Method

“…More recently Lavallée & Hidiroglou algorithm [3] and Gunning & Horgan's (2004) geometric method [4] have been proposed for highly skewed populations whereas Kozak's (2004) random search method [2] and Keskinturk & Er's (2007) genetic algorithm (GA) method [1] have been proposed for even non-skewed populations. Very recently, Brito et.all [6] proposed an exact algorithm for the stratification problem with only proportional allocation based on the concept of minimum path in graphs and they called their method StratPath. Moreover, developed an iterated local search method to solve the stratification problem of variables with any distribution with Neyman allocation [7].All these methods aim to achieve the optimum boundaries that maximise the level of precision or equivalently minimise the variance of the estimate or the sample size required to reach a level of precision and some of them are available in the stratification package stratification for use with the statistical programming environment R [8]; freely available on the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/package=stratification.…”