Author:
Fattorini Lorenzo,Franceschi Sara,Marcheselli Marzia,Pisani Caterina,Pratelli Luca
Abstract
AbstractIn the inverse distance weighting interpolation the interpolated, value is a weighted mean of the sampled values, with weights decreasing with the distances. The most widely adopted class of distance functions is the class of negative powers of order $$\alpha $$
α
and the appropriate choice of the smoothing parameter $$\alpha $$
α
is a crucial issue. In this paper, we give sufficient conditions for the design-based consistency of the inverse distance weighting interpolator when $$\alpha $$
α
is selected by cross-validation techniques, and a pseudo-population bootstrap approach is introduced to estimate the accuracy of the resulting interpolator. A simulation study is performed to empirically confirm the theoritical findings and to investigate the finite-sample properties of the interpolator obtained using leave-one-out cross-validation. Moreover, a comparison with the nearest neighbor interpolator, which is the limiting case for $$\alpha =\infty $$
α
=
∞
, is performed. Finally, the estimation of the surface of the Shannon diversity index of tree diameter at breast height in the experimental watershed of Bonis forest (Southern Italy) is described.
Funder
Ministero dell’Universitá e della Ricerca
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Environmental Science,Statistics and Probability
Cited by
1 articles.
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