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All (3) ((3 results))
- Articles and reports: 12-001-X202600100008Description: This paper introduces an innovative and intuitive finite population sampling method that has been developed using a unique graphical framework. In this approach, first-order inclusion probabilities are represented as bars on a two-dimensional graph. By manipulating the positions of these bars, researchers can create a wide range of different sampling designs. This graphical visualization of sampling designs facilitates the exploration of alternative designs and may simplify certain aspects of the implementation compared to traditional mathematical algorithms. This novel approach holds significant promise for tackling complex challenges in sampling, such as achieving an optimal design. By applying a version of the greedy best-first search algorithm to this graphical approach, the potential for integrating intelligent algorithms into finite population sampling is demonstrated.Release date: 2026-06-29
- Articles and reports: 12-001-X202300100009Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.Release date: 2023-06-30
- 3. Adaptive rectangular sampling: An easy, incomplete, neighbourhood-free adaptive cluster sampling design ArchivedArticles and reports: 12-001-X201600214684Description:
This paper introduces an incomplete adaptive cluster sampling design that is easy to implement, controls the sample size well, and does not need to follow the neighbourhood. In this design, an initial sample is first selected, using one of the conventional designs. If a cell satisfies a prespecified condition, a specified radius around the cell is sampled completely. The population mean is estimated using the \pi-estimator. If all the inclusion probabilities are known, then an unbiased \pi estimator is available; if, depending on the situation, the inclusion probabilities are not known for some of the final sample units, then they are estimated. To estimate the inclusion probabilities, a biased estimator is constructed. However, the simulations show that if the sample size is large enough, the error of the inclusion probabilities is negligible, and the relative \pi-estimator is almost unbiased. This design rivals adaptive cluster sampling because it controls the final sample size and is easy to manage. It rivals adaptive two-stage sequential sampling because it considers the cluster form of the population and reduces the cost of moving across the area. Using real data on a bird population and simulations, the paper compares the design with adaptive two-stage sequential sampling. The simulations show that the design has significant efficiency in comparison with its rival.
Release date: 2016-12-20
Articles and reports (3)
Articles and reports (3) ((3 results))
- Articles and reports: 12-001-X202600100008Description: This paper introduces an innovative and intuitive finite population sampling method that has been developed using a unique graphical framework. In this approach, first-order inclusion probabilities are represented as bars on a two-dimensional graph. By manipulating the positions of these bars, researchers can create a wide range of different sampling designs. This graphical visualization of sampling designs facilitates the exploration of alternative designs and may simplify certain aspects of the implementation compared to traditional mathematical algorithms. This novel approach holds significant promise for tackling complex challenges in sampling, such as achieving an optimal design. By applying a version of the greedy best-first search algorithm to this graphical approach, the potential for integrating intelligent algorithms into finite population sampling is demonstrated.Release date: 2026-06-29
- Articles and reports: 12-001-X202300100009Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.Release date: 2023-06-30
- 3. Adaptive rectangular sampling: An easy, incomplete, neighbourhood-free adaptive cluster sampling design ArchivedArticles and reports: 12-001-X201600214684Description:
This paper introduces an incomplete adaptive cluster sampling design that is easy to implement, controls the sample size well, and does not need to follow the neighbourhood. In this design, an initial sample is first selected, using one of the conventional designs. If a cell satisfies a prespecified condition, a specified radius around the cell is sampled completely. The population mean is estimated using the \pi-estimator. If all the inclusion probabilities are known, then an unbiased \pi estimator is available; if, depending on the situation, the inclusion probabilities are not known for some of the final sample units, then they are estimated. To estimate the inclusion probabilities, a biased estimator is constructed. However, the simulations show that if the sample size is large enough, the error of the inclusion probabilities is negligible, and the relative \pi-estimator is almost unbiased. This design rivals adaptive cluster sampling because it controls the final sample size and is easy to manage. It rivals adaptive two-stage sequential sampling because it considers the cluster form of the population and reduces the cost of moving across the area. Using real data on a bird population and simulations, the paper compares the design with adaptive two-stage sequential sampling. The simulations show that the design has significant efficiency in comparison with its rival.
Release date: 2016-12-20