Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator
Open Access
- 14 June 2021
- journal article
- research article
- Published by Oxford University Press (OUP) in Biometrics
- Vol. 78 (4), 1454-1463
- https://doi.org/10.1111/biom.13505
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.Keywords
This publication has 25 references indexed in Scilit:
- Doubly balanced spatial sampling with spreading and restitution of auxiliary totalsEnvironmetrics, 2012
- Sampling designs for accuracy assessment of land coverInternational Journal of Remote Sensing, 2009
- Use of space-filling curves to select sample locations in natural resource monitoring studiesEnvironmental Monitoring and Assessment, 2008
- Model-Assisted Estimation of Forest Resources With Generalized Additive ModelsJournal of the American Statistical Association, 2007
- Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision BoundariesDiscrete & Computational Geometry, 2005
- Comparison of spatial interpolation methods for the estimation of air quality dataJournal of Exposure Science & Environmental Epidemiology, 2004
- Spatially Balanced Sampling of Natural ResourcesJournal of the American Statistical Association, 2004
- Variable Kernel Density EstimationThe Annals of Statistics, 1992
- An Introduction to Kernel and Nearest-Neighbor Nonparametric RegressionThe American Statistician, 1992
- Consistent Nonparametric RegressionThe Annals of Statistics, 1977