Abstract
The bootstrap is a computer intensive resampling method for calculating measures of accuracy of sample estimates and constructing hypothesis tests. In this paper, a new application of the bootstrap to semi-variogram modeling is proposed. The values resulting from taking at each lag the median of a set of bootstrap empirical semi-variograms is used in the fitting of a model instead of the mean square differences of the classical experimental semi-variogram. This new procedure is iterative and requires only that the user specify the analytical form of the semi-variogram for the attribute and its normal scores. Relative to conventional modeling, the new method checks for self-consistency and performs better with increasingly smaller sample sizes. The procedure is illustrated by using different data subsets sampled from an exhaustive synthetic random field for which the true semi-variogram type and parameters are known.
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Acknowledgments
The work of the first author was supported by research project CGL2010-15498 from the Ministerio de Economía y Competitividad of Spain. The work of the third author was supported by Australian Research Council Discovery Grant DP110014766. Comments by Özgen Karacan, Goeffrey Phelps and by an anonymous reviewer contributed to improve earlier versions of the manuscript.
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Pardo-Igúzquiza, E., Olea, R.A., Dowd, P.A. (2014). Semi-Variogram Model Inference Using a Median Bootstrap Statistics. In: Pardo-Igúzquiza, E., Guardiola-Albert, C., Heredia, J., Moreno-Merino, L., Durán, J., Vargas-Guzmán, J. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32408-6_19
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DOI: https://doi.org/10.1007/978-3-642-32408-6_19
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