Abstract
In this paper, we obtain a saddlepoint approximation for the small sample distribution of several variogram estimators such as the classical Matheron’s estimator, some M-estimators like the robust Huber’s variogram estimator, and also the \(\alpha \)-trimmed variogram estimator. The tail probability approximation obtained is very accurate even for small sample sizes. In the approximations we consider that the observations follow a distribution close to the normal, specifically, a scale contaminated normal model. To obtain the approximations we transform the original observations into a new ones, which can be considered independent if a linearized variogram can be accepted as model for them. To check this, a goodness of fit test for a variogram model is defined in the last part of the paper.
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Acknowledgements
The author is very grateful to the referee and the Editor in Chief for their careful reading and remarks which have improved the paper. This work is partially supported by Grant MTM 2015-67057-P from Ministerio de Economía, Industria y Competitividad (Spain).
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García-Pérez, A. Saddlepoint approximations for the distribution of some robust estimators of the variogram. Metrika 83, 69–91 (2020). https://doi.org/10.1007/s00184-019-00725-6
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DOI: https://doi.org/10.1007/s00184-019-00725-6