Advances and Applications in Statistics
Volume 51, Issue 1, Pages 39 - 57
(July 2017) http://dx.doi.org/10.17654/AS051010039 |
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A GOAL PROGRAMMING APPROACH FOR SAMPLES OVERLAP IN STRATIFIED RANDOM SAMPLING
Nihal Abd El Aty, Mahmoud Rashwan and Ramdan Hamed
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Abstract: Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. In this paper, we present a new method for coordination of samples selected according to stratified random sampling without replacement (SRSWOR) designs. A goal programming model is introduced to determine the samples’ sizes and samples’ allocation when two sample surveys are conducted simultaneously on the same set of units from a stratified population with two strata. In this model, maximization of the expected number of common units in the samples of both surveys (number of overlaps) is introduced as an objective that helps in minimizing costs and time. Besides, the classical goals regarding minimization of cost, time and variances of estimates are also included. A simulation study is conducted in order to assess the suggested method for different number of variables and different levels of dependence between variables. The simulation study results indicated that the suggested model performance satisfies the maximum expected overlap (the absolute upper bound), so our suggested model is a maximal one in different cases. |
Keywords and phrases: sample coordination, overlap, controlled selection, stratified sampling, optimum allocation, goal programming. |
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