An investigation of balanced sampling excluding adjacent units

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2002-01-01
Authors
Wright, James
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Commonly, in environmental and ecological populations, neighboring units within a finite population may provide similar information. In an attempt to obtain the most informative picture of a population, researchers may not want to collect information from similar units within the obtained sample. Moreover, when sampling from such populations, the selection of dispersed units may result in a reduction in the variance of estimators.;Hedayat, Rao, and Stufken (1988a and 1988b) introduced balanced sampling designs for the exclusion of contiguous units. Under the assumption that contiguous units provided similar information, finite populations of N units arranged in a circular, one dimensional ordering were considered. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated. Stufken (1993) extended the ideas of balanced sampling avoiding contiguous units to balanced sampling avoiding adjacent units---units that are within a spaces of each other---from circularly ordered populations and provided necessary conditions for the existence of such sampling plans.;In this paper, two direct search algorithms for identifying generators of cyclical balanced sampling plans excluding adjacent units from circularly ordered populations are detailed. Generators for plans with alpha = 1 and n ≤ 15 and with alpha = 2 and 3 with n ≤ 10 are presented, including the first known sets of generators of plans for n ≥ 9 with alpha = 1, n ≥ 6 with alpha = 2, and n ≥ 5 with alpha = 3. Furthermore, the necessary conditions for existence of balanced sampling plans excluding adjacent units from circularly ordered populations are shown to be sufficient for n = 5 and 6 with alpha = 1, n = 3, 4, and 5 with alpha = 2, and n = 3 and 4 with alpha = 3. Techniques for obtaining supports of balanced sampling plans excluding adjacent units from linearly ordered populations using plans from circularly ordered populations, and vice versa, are also presented. In addition, various sampling schemes involving balanced sampling plans excluding adjacent units from circularly ordered populations and variance approximation techniques are compared through a simulation study.

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