García Pérez, Alfonso2024-05-202024-05-202022-05-232227-7390https://doi.org/10.3390/math10101785https://hdl.handle.net/20.500.14468/11927The spatio-temporal variogram is an important factor in spatio-temporal prediction through kriging, especially in fields such as environmental sustainability or climate change, where spatio-temporal data analysis is based on this concept. However, the traditional spatio-temporal variogram estimator, which is commonly employed for these purposes, is extremely sensitive to outliers. We approach this problem in two ways in the paper. First, new robust spatio-temporal variogram estimators are introduced, which are defined as M-estimators of an original data transformation. Second, we compare the classical estimate against a robust one, identifying spatio-temporal outliers in this way. To accomplish this, we use a multivariate scale-contaminated normal model to produce reliable approximations for the sample distribution of these new estimators. In addition, we define and study a new class of M-estimators in this paper, including real-world applications, in order to determine whether there are any significant differences in the spatio-temporal variogram between two temporal lags and, if so, whether we can reduce the number of lags considered in the spatio-temporal analysis.enAtribución-NoComercial-SinDerivadas 4.0 Internacionalinfo:eu-repo/semantics/openAccessartículorobust statisticsspatio-temporal outliersvon Mises expansionssaddlepoint approximations