Exploring Spatial Continuity with Wendland’s Covariance Functions
a geostatistical approach
DOI:
https://doi.org/10.5540/03.2025.011.01.0399Palabras clave:
Compact Support, Geostatistics, Sparse Matrix, Spatial VariabilityResumen
This study explores spatial continuity using Wendland’s covariance functions in geostatistical modeling. Wendland’s covariance family, defined within a compact support, offers flexibility with a smoothing parameter, competing with the well-known Matérn family. Expressions for covariance functions and a spatial dependency index are provided, along with sensitivity analysis using local influential diagnostics. Jackknife-after-Bootstrap resamples establish reference levels for potential influence detection. An application to soybean yield data validates the methodology.
Descargas
Citas
M. Bevilacqua, T. Faouzi, R. Furrer, and E. Porcu. “Estimation and prediction using generalized wendland covariance functions under fixed domain asymptotics”. In: The Annals of Statistics 47.2 (2019), pp. 828–856.
A. Chernih and S. Hubbert. “Closed form representations and properties of the generalised Wendland functions”. In: Journal of Approximation Theory 177 (2014), pp. 17–33.
A. Chernih, I. H. Sloan, and R. S. Womersley. “Wendland functions with increasing smoothness converge to a Gaussian”. In: Advances in Computational Mathematics 40.1 (2014), pp. 185–200.
R. D. Cook. “Assessment of local influence”. In: Journal of the Royal Statistical Society. Series B (Methodological), 133–169 (1986).
N. A. C. Cressie. Statistics for spatial data. Wiley series in probability, mathematical statistics. Applied probability, and statistics section, 1993.
P. J. Diggle and P. J. Ribeiro. Model-based Geostatistics. 2007.
T. Gneiting. “Compactly supported correlation functions”. In: Journal of Multivariate Analysis 83.2 (2002), pp. 493–508.
M. A. U. Opazo, J. A. Borssoi, and M. Galea. “Influence diagnostics in Gaussian spatial linear models”. In: Journal of Applied Statistics 39.3 (2012), pp. 615–630.
M. Santos. “Uma releitura inferencial e análise de diagnósticos em modelos geoestatísticos”. PhD thesis. Universidade Federal de Pernambuco, 2022.
E. Seidel and M. S. Oliveira. “A classification for a geostatistical index of spatial dependence”. In: Revista Brasileira de Ciência do Solo 40 (2016).
E. J. Seidel and M. S. Oliveira. “Novo índice geoestatístico para a mensuração da dependência espacial”. In: Revista Brasileira de Ciência do Solo 38.3 (2014), pp. 699–705.
H. Wendland. “Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree”. In: Advances in Computational Mathematics 4.1 (1995), pp. 389–396.
Z. Wu. “Compactly supported positive definite radial functions”. In: Advances in Computational Mathematics 4.1 (1995), p. 283.
V. P. Zastavnyi. “On some properties of Buhmann functions”. In: Ukrainian Mathematical Journal 58.8 (2006), pp. 1184–1208.
