Persona: García Pérez, Alfonso
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García Pérez
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Publicación On robustness for spatio-temporal data(MDPI, 2022-05-23) García Pérez, AlfonsoThe 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.Publicación Trimmed spatio-temporal variogram estimator(Springer, 2022-08-25) García Pérez, AlfonsoThe spatio-temporal variogram is the key element in spatiotemporal prediction based on kriging, but the classical estimator of this parameter is very sensitive to outliers. In this contributed paper we propose a trimmed estimator of the spatio-temporal variogram as a robust estimator. We obtain an accurate approximation of its distribution with small samples sizes and a scale contaminated normal model.We conclude with an example with real data.Publicación A New Estimator: Median of the Distribution of the Mean in Robustness(MDPI, 2023-06-14) García Pérez, AlfonsoIn some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution 𝐹𝑥̲ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of 𝐹𝑥̲ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, 𝑀𝑑𝑀. This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW.Publicación New robust cross-variogram estimators and approximations of their distributions based on saddlepoint techniques(MDPI, 2021-04-01) García Pérez, AlfonsoLet 𝐙(𝐬)=(𝑍1(𝐬),…,𝑍𝑝(𝐬))𝑡 be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between the p random components of 𝐙 with the correlation coefficients and measure the spatial dependence with variograms. If two of the 𝐙 components are correlated, the spatial information provided by one of them can improve the information of the other. To capture this association, both within components of 𝐙(𝐬)and across 𝐬, we use a cross-variogram. Only two robust cross-variogram estimators have been proposed in the literature, both by Lark, and their sample distributions were not obtained. In this paper, we propose new robust cross-variogram estimators, following the location estimation method instead of the scale estimation one considered by Lark, thus extending the results obtained by García-Pérez to the multivariate case. We also obtain accurate approximations for their sample distributions using saddlepoint techniques and assuming a multivariate-scale contaminated normal model. The question of the independence of the transformed variables to avoid the usual dependence of spatial observations is also considered in the paper, linking it with the acceptance of linear variograms and cross-variograms.Publicación Variogram model selection(Springer, 2022-06-28) García Pérez, AlfonsoA common problem in geostatistics is variogram estimation, in order to choose an acceptable model for kriging. Nevertheless, there is no standard method, first, to test if a particular model can be accepted as valid and, second, to choose among several competing variogram models. The problem is even more complex if, in addition, there are outliers in the data. In this paper we propose to use the distribution of some classical and robust variogram estimators to test, first, the validity of a particular model, accepting it if the p-value of the test, with this particular model as null hypothesis, is large enough and, second, to compare several competing models, choosing the model with the largest p-value among several acceptable models.