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Ordered Spatial Sampling by Means of the Traveling Salesman Problem

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  • Maria Michela Dickson
  • Yves Tille'

Abstract

In recent years, spatial sampling has been the subject of a flourishing literature. Its use had become widespread due to the availability of topographical information about statistical units, especially in the environmental context. New algorithms enable us to take advantage of spatial locations directly. In this paper, we present a new way of using spatial information by using traditional sampling techniques as systematic sampling. By means of a famous optimization method, the Traveling Salesman Problem, it is possible to order the statistical units in a way that preserves the spatial correlation. Next ordered sampling methods are applied on the statistical units. Therefore we can render spatial some non-spatial methods. An economic application on real data is presented and different spatial and non-spatial methods are tested. Results are compared in terms of variance estimation and spatial balance, in order to establish the possibility of spatializing traditional sampling methods and of implementing them on data of different nature, among which economic ones.

Suggested Citation

  • Maria Michela Dickson & Yves Tille', 2015. "Ordered Spatial Sampling by Means of the Traveling Salesman Problem," DEM Discussion Papers 2015/06, Department of Economics and Management.
    • Handle: RePEc:trn:utwpem:2015/06
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    1. Anton Grafström & Yves Tillé, 2013. "Doubly balanced spatial sampling with spreading and restitution of auxiliary totals," Environmetrics, John Wiley & Sons, Ltd., vol. 24(2), pages 120-131, March.
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    5. Jean-Claude Deville & Yves Tille, 2004. "Efficient balanced sampling: The cube method," Biometrika, Biometrika Trust, vol. 91(4), pages 893-912, December.
    6. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    7. Hahsler, Michael & Hornik, Kurt, 2007. "TSPInfrastructure for the Traveling Salesperson Problem," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i02).
    8. Stevens, Don L. & Olsen, Anthony R., 2004. "Spatially Balanced Sampling of Natural Resources," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 262-278, January.
    9. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
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    Cited by:

    1. Chauvet, Guillaume & Ruiz-Gazen, Anne, 2017. "A comparison of pivotal sampling and unequal probability sampling with replacement," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 1-5.
    2. Guillaume Chauvet & Ronan Le Gleut, 2021. "Inference under pivotal sampling: Properties, variance estimation, and application to tesselation for spatial sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 108-131, March.
    3. Yves Tillé, 2022. "Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials," International Statistical Review, International Statistical Institute, vol. 90(3), pages 481-498, December.
    4. Raphaël Jauslin & Yves Tillé, 2020. "Spatial Spread Sampling Using Weakly Associated Vectors," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 431-451, September.
    5. Fulvia Mecatti & Charalambos Sismanidis & Emanuela Furfaro & Pier Luigi Conti, 2023. "Sequential adaptive strategies for sampling rare clustered populations," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1659-1693, December.
    6. B. L. Robertson & O. Ozturk & O. Kravchuk & J. A. Brown, 2022. "Spatially Balanced Sampling with Local Ranking," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 622-639, December.
    7. Huan Xie & Fang Wang & Yali Gong & Xiaohua Tong & Yanmin Jin & Ang Zhao & Chao Wei & Xinyi Zhang & Shicheng Liao, 2022. "Spatially Balanced Sampling for Validation of GlobeLand30 Using Landscape Pattern-Based Inclusion Probability," Sustainability, MDPI, vol. 14(5), pages 1-19, February.
    8. Roberto Benedetti & Federica Piersimoni & Paolo Postiglione, 2017. "Spatially Balanced Sampling: A Review and A Reappraisal," International Statistical Review, International Statistical Institute, vol. 85(3), pages 439-454, December.
    9. R. Benedetti & F. Piersimoni & P. Postiglione, 2017. "Alternative and complementary approaches to spatially balanced samples," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 249-264, December.

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    Keywords

    sampling methods; TSP; variance estimation; spatial balance;
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