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From model selection to maps: A completely design‐based data‐driven inference for mapping forest resources

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  • Rosa Maria Di Biase
  • Lorenzo Fattorini
  • Sara Franceschi
  • Mirko Grotti
  • Nicola Puletti
  • Piermaria Corona

Abstract

A completely data‐driven, design‐based sampling strategy is proposed for mapping a forest attribute within the spatial units tessellating a survey region. Based on sample data, a model is selected, and model parameters are estimated using least‐squares criteria for predicting the attribute of interest within units as a linear function of a set of auxiliary variables. The spatial interpolation of residuals arising from model predictions is performed by inverse distance weighting. The leave‐one‐out cross validation procedure is adopted for selecting the smoothing parameter used for interpolation. The densities of the attributes of interest within units are estimated by summing predictions and interpolated residuals. Finally, density estimates are rescaled to match the total estimate over the survey region obtained by the traditional regression estimator with the total estimate obtained from the map as the sum of the density estimates within units. A bootstrap procedure accounts for the uncertainty. The consistency of the strategy is proven by incorporating previous results. A simulation study is performed and an application for mapping wood volume densities in the forest estate of Rincine (Central Italy) is described.

Suggested Citation

  • Rosa Maria Di Biase & Lorenzo Fattorini & Sara Franceschi & Mirko Grotti & Nicola Puletti & Piermaria Corona, 2022. "From model selection to maps: A completely design‐based data‐driven inference for mapping forest resources," Environmetrics, John Wiley & Sons, Ltd., vol. 33(7), November.
    • Handle: RePEc:wly:envmet:v:33:y:2022:i:7:n:e2750
    DOI: 10.1002/env.2750
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    1. 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.
    2. Lorenzo Fattorini & Piermaria Corona & Gherardo Chirici & Maria Chiara Pagliarella, 2015. "Design‐based strategies for sampling spatial units from regular grids with applications to forest surveys, land use, and land cover estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 26(3), pages 216-228, May.
    3. Little R.J., 2004. "To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 546-556, January.
    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.
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