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Design‐based properties of the nearest neighbor spatial interpolator and its bootstrap mean squared error estimator
Author(s) -
Fattorini Lorenzo,
Marcheselli Marzia,
Pisani Caterina,
Pratelli Luca
Publication year - 2022
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13505
Subject(s) - estimator , mean squared error , statistics , k nearest neighbors algorithm , mathematics , computer science , artificial intelligence
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.