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 α-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.
This is an Accepted Manuscript of an article published by Springer in "Metrika 83, 69–91 (2020)" on 26-06-2019, available at: https://doi.org/10.1007/s00184-019-00725-6
Notas adicionales
Este es el manuscrito aceptado del artículo publicado por Springer en "Metrika 83, 69–91 (2020)" el 26-06-2019, disponible en línea: https://doi.org/10.1007/s00184-019-00725-6
