Abstract
The spatio-temporal variogram is the key element in spatio-temporal prediction based on kriging, but the classical estimator of this parameter is very sensitive to outliers. In this contributed paper we propose a trimmed estimator of the spatio-temporal variogram as a robust estimator. We obtain an accurate approximation of its distribution with small samples sizes and a scale contaminated normal model. We conclude with an example with real data.
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References
Cressie, N.A.C.: Statistics for Spatial Data. Wiley, New York (1993)
García-Pérez, A.: A von Mises approximation to the small sample distribution of the trimmed mean. Metrika 79(4), 369–388 (2016)
García-Pérez, A.: Saddlepoint approximations for the distribution of some robust estimators of the variogram. Metrika 83, 69–91 (2020)
García-Pérez, A.: New robust cross-variogram estimators and approximations for their distributions based on saddlepoint techniques. Mathematics 9, 762 (2021)
García-Pérez, A.: Variogram model selection. In: Balakrishnan, N., Gil, M.A., Martin, N., Morales, D., Pardo, M.C. (eds.) Trends in Mathematical, Information and Data Sciences, Studies in Systems, Decision and Control, vol. 445. Springer, Heidelberg (2022a). https://doi.org/10.1007/978-3-031-04137-2_3
García-Pérez, A.: On robustness for spatio-temporal data. Mathematics 10, 1785 (2022)
Huber, P.J., Ronchetti, E.M.: Robust Statistics, 2nd edn. Wiley, New York (2009)
Varouchakis, E.A., Hristopulos, D.T.: Comparison of spatiotemporal variogram functions based on a sparse dataset of groundwater level variations. Spat. Stat. 34, 1–18 (2019)
von Mises, R.: On the asymptotic distribution of differentiable statistical functions. Ann. Math. Stat. 18, 309–348 (1947)
Wikle, C.K., Zammit-Mangion, A., Cressie, N.: Spatio-Temporal Statistics with R. Chapman & Hall/CRC, New York (2019)
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The author is very grateful to the referee and to the Ministerio de Ciencia e Innovación.
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García-Pérez, A. (2023). Trimmed Spatio-Temporal Variogram Estimator. In: García-Escudero, L.A., et al. Building Bridges between Soft and Statistical Methodologies for Data Science . SMPS 2022. Advances in Intelligent Systems and Computing, vol 1433. Springer, Cham. https://doi.org/10.1007/978-3-031-15509-3_23
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DOI: https://doi.org/10.1007/978-3-031-15509-3_23
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