Title: Saddlepoint approximations for the distribution of some robust estimators of the variogram
Authors: Alfonso Garcia-Perez - UNED (Spain) [presenting]
Abstract: The estimation of the variogram is a very important issue in geostatistics where a random variable is observed at some fixed locations. Matheron's estimator is the classical variogram estimator used in spatial statistical applications. There are also some robust versions, but their distributions (or some approximations of them) have not been studied in detail. Besides, although the sample size in geostatistics is not usually small, because the estimation of the variogram is made for each lag $h$, the number of observations used in each of these estimations, could be small. Hence, a saddlepoint approximation for the distribution of the variogram estimator should be suitable. We obtain a von Mises plus saddlepoint approximation for the distribution of these estimators, assuming that the sequence of the observations verifies the intrinsic stationarity property and that they follow a model distribution near to the normal; specifically a contaminated normal model. The accuracy of these approximations is illustrated with some Monte Carlo experiments. The approximation so obtained is used to analyze the robust properties of several variogram estimators. We shall also use it to test the variogram model and to analyze the required independence of the transformed observations used in the saddlepoint approximation.