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

Area of Science:

• Spatial statistics
• Geostatistics
• Environmental science

Background:

• Nearest neighbor methods are used for spatial interpolation.
• Design-based perspective assumes fixed populations and sampling-induced uncertainty.
• Existing methods lack robust error estimation for population mapping.

Purpose of the Study:

• To derive conditions for the consistency of nearest neighbor interpolators.
• To propose a novel pseudopopulation bootstrap estimator for root mean squared errors.
• To assess the performance of these methods in population mapping.

Main Methods:

• Design-based statistical framework for spatial interpolation.
• Derivation of consistency conditions for nearest neighbor algorithms.
• Development of a pseudopopulation bootstrap method for error estimation.
• Simulation studies to evaluate theoretical findings.

Main Results:

• Nearest neighbor interpolators demonstrate design-based consistency under specific sampling schemes.
• Consistency is proven for schemes common in environmental and forest surveys.
• The proposed bootstrap estimator provides a reliable method for assessing interpolation uncertainty.
• Simulation results support the theoretical derivations.

Conclusions:

• Nearest neighbor spatial interpolation is a statistically sound approach for mapping populations.
• The study provides theoretical guarantees and practical tools for reliable spatial data analysis.
• Findings are applicable to environmental monitoring, resource management, and other survey applications.