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k-step adaptive cluster sampling with Horvitz-Thompson estimator

International Journal of Biomathematics 2018年第2期11卷 299-317页

作者： Quangyu Zhu Liyong Fu Central South University of Forestry and Technology 498 Shaoshan Nanlu Changsha 410004 Hunan P. R. China Research Institute of ForestResource Information Techniques Chinese Academy of Forestry Beijing 100091 P. R. China Center for Statistical Genetics Pennsylvania State University Loc T3436 Mailcode CH69500 University Drive Hershey PA 17033 USA

Adaptive cluster sampling （ACS） has been widely used for data collection of environment and natural resources. However, the randomness of its final sample size often impedes the use of this method. To control the final sample sizes, in this study, a k-step ACS based on Horvitz-Thompson （HT） estimator was developed and an unbiased estimator was derived. The k-step ACS-HT was assessed first using a simulated example and then using a real survey for numbers of plants for three species that were characterized by clustered and patchily spatial distributions. The effectiveness of this sampling design method was assessed in comparison with ACS Hansen-Hurwitz （ACS-HH） and ACS- HT estimators, and k-step ACS-HT estimator. The effectiveness of using different k- step sizes was also compared. The results showed that k-step ACS^HT estimator was most effective and ACS-HH was the least. Moreover, stable sample mean and variance estimates could be obtained after a certain number of steps, but depending on plant species, k-step ACS without replacement was slightly more effective than that with replacement. In k-step ACS, the variance estimate of one-step ACS is much larger than other k-step ACS （k 〉 1）, but it is smaller than ACS. This implies that k-step ACS is more effective than traditional ACS, besides, the final sample size can be controlled easily in population with big clusters.

关键词： finalized sample size k-step adaptive cluster sampling plant species sample design inlprovement unbiased estimator.

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