IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v78y2022i4p1454-1463.html
   My bibliography  Save this article

Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator

Author

Listed:
  • Lorenzo Fattorini
  • Marzia Marcheselli
  • Caterina Pisani
  • Luca Pratelli

Abstract

Nearest neighbor spatial interpolation for mapping continuous populations and finite populations of areas or units is approached from a design‐based perspective, that is, populations are fixed, and uncertainty stems from the sampling scheme adopted to select locations. We derive conditions for design‐based pointwise and uniform consistency of the nearest neighbor interpolators. We prove that consistency holds under certain schemes that are widely applied in environmental and forest surveys. Furthermore, we propose a pseudopopulation bootstrap estimator of the root mean squared errors of the interpolated values. Finally, a simulation study is performed to assess the theoretical results.

Suggested Citation

  • Lorenzo Fattorini & Marzia Marcheselli & Caterina Pisani & Luca Pratelli, 2022. "Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator," Biometrics, The International Biometric Society, vol. 78(4), pages 1454-1463, December.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:4:p:1454-1463
    DOI: 10.1111/biom.13505
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13505
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13505?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    2. L Fattorini & M Marcheselli & C Pisani & L Pratelli, 2018. "Design-based maps for continuous spatial populations," Biometrika, Biometrika Trust, vol. 105(2), pages 419-429.
    3. 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.
    4. L. Fattorini & M. Marcheselli & L. Pratelli, 2018. "Design-Based Maps for Finite Populations of Spatial Units," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 686-697, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomasz Bąk, 2021. "Spatial sampling methods modified by model use," Statistics in Transition New Series, Polish Statistical Association, vol. 22(2), pages 143-154, June.
    2. Sara Franceschi & Rosa Maria Di Biase & Agnese Marcelli & Lorenzo Fattorini, 2022. "Some Empirical Results on Nearest-Neighbour Pseudo-populations for Resampling from Spatial Populations," Stats, MDPI, vol. 5(2), pages 1-16, April.
    3. Robertson, Blair & Price, Chris, 2024. "One point per cluster spatially balanced sampling," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    4. Wilmer Prentius, 2024. "Locally correlated Poisson sampling," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.
    5. Maria Michela Dickson & Yves Tillé, 2016. "Ordered spatial sampling by means of the traveling salesman problem," Computational Statistics, Springer, vol. 31(4), pages 1359-1372, December.
    6. ak Tomasz B, 2021. "Spatial sampling methods modified by model use," Statistics in Transition New Series, Statistics Poland, vol. 22(2), pages 143-154, June.
    7. Lorenzo Fattorini & Timothy G. Gregoire & Sara Trentini, 2018. "The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 358-373, September.
    8. Matei Alina, 2021. "Book Review," Journal of Official Statistics, Sciendo, vol. 37(4), pages 1079-1081, December.
    9. 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.
    10. Cindy L. Yu & Jie Li & Michael G. Karl & Todd J. Krueger, 2020. "Obtaining a Balanced Area Sample for the Bureau of Land Management Rangeland Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 250-275, June.
    11. Steen Magnussen & Johannes Breidenbach, 2020. "Retrieval of among-stand variances from one observation per stand," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 66(4), pages 133-149.
    12. Pommerening, Arne & Szmyt, Janusz & Zhang, Gongqiao, 2020. "A new nearest-neighbour index for monitoring spatial size diversity: The hyperbolic tangent index," Ecological Modelling, Elsevier, vol. 435(C).
    13. 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.
    14. Gideon Minua Kwaku Ampofo & Prosper Basommi Laari & Emmanuel Opoku Ware & Williams Shaw, 2023. "Further investigation of the total natural resource rents and economic growth nexus in resource-abundant sub-Saharan African countries," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 36(1), pages 97-121, January.
    15. Meredith L Flash & Adelene S M Wong & Mark A Stevenson & James R Gilkerson, 2020. "Barriers to entering race training before 4 years of age for Thoroughbred horses born in the 2014 Australian foal crop," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-15, August.
    16. Thomas Welchowski & Kelly O. Maloney & Richard Mitchell & Matthias Schmid, 2022. "Techniques to Improve Ecological Interpretability of Black-Box Machine Learning Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 175-197, March.
    17. Alice Bartolini & Rosa Maria Di Biase & Lorenzo Fattorini & Sara Franceschi & Agnese Marcelli, 2021. "Design-based mapping of plant species presence, association and richness by nearest-neighbor interpolation," Department of Economics University of Siena 854, Department of Economics, University of Siena.
    18. Maria Michela Dickson & Giuseppe Espa & Diego Giuliani, 2016. "Incomplete geocoding and spatial sampling: the effects of locational errors on population total estimation," DEM Working Papers 2016/04, Department of Economics and Management.
    19. Robertson, B.L. & Reale, M. & Price, C.J. & Brown, J.A., 2021. "Quasi-random ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 171(C).
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:78:y:2022:i:4:p:1454-1463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.